(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 340854, 9905]*) (*NotebookOutlinePosition[ 341568, 9929]*) (* CellTagsIndexPosition[ 341524, 9925]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Population Biology How accurate is mark-recapture?\ \>", "Subtitle", TextAlignment->Center], Cell[TextData[{ "\tIn the study of various species, it is often important for biologists to \ know, or at least estimate, the number of individuals in a given area (eg. \ the number of bison in Yellowstone State Park, or the number of trout in \ Crater Lake). One common method is to actually capture some of the \ individuals and then release them back into the population with some sort of \ permanent mark or tag that indicates their capture. Some time later, a \ second round of captures are made. Biologists can then estimate the total \ size of the population based on the number of newly captured individuals that \ already have tags.\n\tOne basic mathematical assumption of this method is \ that individual creatures are caught at random, i.e. that no particular \ creature has a better chance of getting caught than another. In the \ following, we will use ", StyleBox["Mathematica", FontSlant->"Italic"], " to mimic a the random selection of individual creatures (using fish as an \ example) from the entire population in a particular habitat (using a pond as \ the example).\t" }], "Text", FontSize->14], Cell[TextData[{ StyleBox["\tLet's create a virtual pond. The pond will have a certain \ number of fish in it, which will be represented by the ", FontSize->14], StyleBox["parameter", FontSize->14, FontSlant->"Italic"], StyleBox[" ", FontSize->14], StyleBox["Popsize", "Input", FontSize->14], StyleBox[". For now, we will set the number of fish at a small value, say \ 23.", FontSize->14] }], "Text"], Cell[BoxData[ \(\(PopSize\ = \ 23;\)\)], "Input"], Cell[TextData[{ StyleBox["\tThere are ", FontSize->14], StyleBox["PopSize", "Input", FontSize->14], StyleBox[" fish in the pond, some of which will eventually be tagged. A \ good way to keep track of this is to use a ", FontSize->14], StyleBox["Mathematica", FontSize->14, FontSlant->"Italic"], StyleBox[" list, which can be created using the ", FontSize->14], StyleBox["Table", "Input", FontSize->14], StyleBox[" function. The first part of the table function describes the ", FontSize->14], StyleBox["values ", FontSize->14, FontSlant->"Italic"], StyleBox["to include in the list, the second portion is itself a list that \ determines the ", FontSize->14], StyleBox["length", FontSize->14, FontSlant->"Italic"], StyleBox[" of the table. For example:", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Table[\ "\", {3}]\)], "Input"], Cell[BoxData[ \({"Blind Mouse", "Blind Mouse", "Blind Mouse"}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tAs all the fish in the pond are currently untagged, we will \ generate a list where each element tells the status of a particular fish, in \ this case ", FontSize->14], StyleBox["\"Untagged\"", "Input", FontSize->14], StyleBox[". \nWe will refer to this list as our ", FontSize->14], StyleBox["Population", "Input", FontSize->14], StyleBox[". Notice that there is one element for\neach of the ", FontSize->14], StyleBox["PopSize", "Input", FontSize->14], StyleBox[" (= 23) fish. ", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(PopSize = \ 23;\)\), "\[IndentingNewLine]", \(Population\ = \ Table["\", {PopSize}]\)}], "Input"], Cell[BoxData[ \({"Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged"}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tAt any time we can look at the status of a particular fish in \ the ", FontSize->14], StyleBox["Population", "Input", FontSize->14], StyleBox[" by giving its location in the list, using an ", FontSize->14], StyleBox["index", FontSize->14, FontSlant->"Italic"], StyleBox[". For example, the fish associated with list element number one \ is, as expected, \"", FontSize->14], StyleBox["Untagged", "Input", FontSize->14], StyleBox["\".", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Population[\([1]\)]\)], "Input"], Cell[BoxData[ \("Untagged"\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tIt's time to go fishing! Here we will add another parameter, ", FontSize->14], StyleBox["NumFirstCatch", "Input", FontSize->14], StyleBox[", denoting the number of fish we catch and tag with the first \ capture-and-release.", FontSize->14] }], "Text"], Cell[BoxData[ \(\(NumFirstCatch\ = \ 7;\)\)], "Input"], Cell[TextData[{ StyleBox["\tSo seven fish now need to be labeled \"Tagged\". We can do \ this by using\n", FontSize->14], StyleBox["ReplacePart", "Input", FontSize->14], StyleBox[" to change the list. ", FontSize->14], StyleBox["ReplacePart ", "Input", FontSize->14], StyleBox["requires three inputs: the list, the new part, and the place in \ the list to be replaced.", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(ReplacePart[Population, "\", 3]\)], "Input"], Cell[BoxData[ \({"Untagged", "Untagged", "Tagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged"}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\t", FontSize->14], StyleBox["ReplacePart ", "Input", FontSize->14], StyleBox["actually creates a whole new list. To actually change the ", FontSize->14], StyleBox["Population", "Input", FontSize->14], StyleBox[", we need to set it equal to the result of ", FontSize->14], StyleBox["ReplacePart", "Input", FontSize->14], StyleBox[".", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Population\ = \ ReplacePart[Population, "\", 1]\)], "Input"], Cell[BoxData[ \({"Tagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged"}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tWe want to repeat this process some number of times equal to ", FontSize->14], StyleBox["NumFirstCatch ", "Input", FontSize->14], StyleBox["(in this case a total of seven times). We let ", FontSize->14], StyleBox["Mathematica", FontSize->14, FontSlant->"Italic"], StyleBox[" do the work for us by using a ", FontSize->14], StyleBox["loop ", FontSize->14, FontSlant->"Italic"], StyleBox["function. One common loop function takes the form ", FontSize->14], StyleBox["Do[", "Input", FontSize->14], StyleBox["expr,", "Input", FontSize->14, FontSlant->"Italic"], StyleBox["{i,", "Input", FontSize->14], StyleBox["imin,imax", "Input", FontSize->14, FontSlant->"Italic"], StyleBox["}]", "Input", FontSize->14], StyleBox[". The loop uses a ", FontSize->14], StyleBox["counter", FontSize->14, FontSlant->"Italic"], StyleBox[", in this case represented by the variable ", FontSize->14], StyleBox["i", "Input", FontSize->14], StyleBox[", to count from ", FontSize->14], StyleBox["imin", "Input", FontSize->14, FontSlant->"Italic"], StyleBox[" to ", FontSize->14], StyleBox["imax", "Input", FontSize->14, FontSlant->"Italic"], StyleBox[", each time evaluating ", FontSize->14], StyleBox["expr", "Input", FontSize->14, FontSlant->"Italic"], StyleBox[". So, to tag each of the first ", FontSize->14], StyleBox["NumFirstCatch ", "Input", FontSize->14], StyleBox["(= 7) fish in our population we use the counter ", FontSize->14], StyleBox["i", "Input", FontSize->14], StyleBox[" inside the ", FontSize->14], StyleBox["ReplacePart", "Input", FontSize->14], StyleBox[" statement, which is inside a\n", FontSize->14], StyleBox["Do", "Input", FontSize->14], StyleBox[" loop. ", FontSize->14] }], "Text"], Cell[BoxData[{ \(\(PopSize\ = \ 23;\)\), "\[IndentingNewLine]", \(\(NumFirstCatch\ = \ 7;\)\), "\[IndentingNewLine]", \(\(Population\ = \ Table["\", {PopSize}];\)\), "\[IndentingNewLine]", \(\(Do[\[IndentingNewLine]Population\ = \ ReplacePart[Population, "\", i], \[IndentingNewLine]{i, 1, NumFirstCatch}];\)\)}], "Input"], Cell[TextData[{ StyleBox["\tNotice that our ", FontSize->14], StyleBox["Population", "Input", FontSize->14], StyleBox[" now has seven \"", FontSize->14], StyleBox["Tagged", "Input", FontSize->14], StyleBox["\" fish.", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Population\)], "Input"], Cell[BoxData[ \({"Tagged", "Tagged", "Tagged", "Tagged", "Tagged", "Tagged", "Tagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged"}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tTime to go fishing again! This time we will plan to catch a few \ more (twelve) fish, by setting a variable ", FontSize->14], StyleBox["NumSecondCatch", "Input", FontSize->14], StyleBox[".", FontSize->14] }], "Text"], Cell[BoxData[ \(\(NumSecondCatch\ = \ 12;\)\)], "Input"], Cell[TextData[{ StyleBox["\tThis time, however, we have to be careful about how we catch \ the fish. If we assume the first fish we catch is the first fish in the \ list, we will automatically catch a tagged fish. The process assumes that \ the fish are caught at random, so we must use a random process, something \ equivalent to the roll of a die, to determine which fish we 'catch'.", FontSize->14], "\n", StyleBox["\t", FontSize->14], StyleBox["Mathematica", FontSize->14, FontSlant->"Italic"], StyleBox[" can generate a wide variety of random numbers. The basic\n\ command ", FontSize->14], StyleBox["Random[]", "Input", FontSize->14], StyleBox[" gives an essentially random number from 0 to 1.", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Random[]\)], "Input"], Cell[BoxData[ \(0.9975438750621808`\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tWith an ", FontSize->14], StyleBox["integer", "Input", FontSize->14], StyleBox[" specification, ", FontSize->14], StyleBox["Mathematica", FontSize->14, FontSlant->"Italic"], StyleBox[" will return either 0 or 1, with equal probability.", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Random[Integer]\)], "Input"], Cell[BoxData[ \(1\)], "Output"] }, Open ]], Cell[TextData[StyleBox["\tBy adding a short list with minimum and maximum \ values, we can specify the random selection of one integer within a \ particular range.", FontSize->14]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Random[Integer, {5, 10}]\)], "Input"], Cell[BoxData[ \(7\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tTo choose a particular fish in our ", FontSize->14], StyleBox["Population", "Input", FontSize->14], StyleBox[", we set an variable,\n", FontSize->14], StyleBox["CaughtThisOne", "Input", FontSize->14], StyleBox[", equal to a random number from 1 to the size of the population \ (", FontSize->14], StyleBox["PopSize", "Input", FontSize->14], StyleBox[").", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(CaughtThisOne\ = \ Random[Integer, {1, PopSize}]\)], "Input"], Cell[BoxData[ \(15\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tWe can then use ", FontSize->14], StyleBox["CaughtThisOne", "Input", FontSize->14], StyleBox[" as an index to see the status of the particular fish we have \ caught.", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Population[\([CaughtThisOne]\)]\)], "Input"], Cell[BoxData[ \("Untagged"\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tWe could catch more fish (perhaps as many as ", FontSize->14], StyleBox["NumSecondCatch", "Input", FontSize->14], StyleBox["?) and make a list of indices for fish we catch, by again using \ our ", FontSize->14], StyleBox["Table", "Input", FontSize->14], StyleBox[" function. ", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Table[\[IndentingNewLine]\t CaughtThisOne\ = Random[Integer, {1, PopSize}], \[IndentingNewLine]\t{NumSecondCatch}]\)], "Input"], Cell[BoxData[ \({3, 19, 2, 20, 8, 11, 23, 11, 10, 21, 9, 10}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tNow we must be careful! Look closely at the ", FontSize->14], StyleBox["SecondCatch", "Input", FontSize->14], StyleBox[" list. Unfortunately, there is a good chance (97%) that you \ caught the same fish (i.e. picked the same index) more than once! (If not, \ you can evaluate the command above again...)\n\tIs this consistent with our \ physical system? Are we throwing the fish back in as we catch them so we ", FontSize->14], StyleBox["could", FontSize->14, FontWeight->"Bold"], StyleBox[" catch them twice in the same catch? Probably not, so we need to \ fix our computational model to match the real system.\n\t\n\tNotice that \ everytime we catch a fish the second time, we remove it from the lake (at \ least temporarily), leaving one fewer fish in the lake. To keep track of this \ we make two new lists, ", FontSize->14], StyleBox["StillInLake", "Input", FontSize->14], StyleBox[" and ", FontSize->14], StyleBox["SecondCatch", "Input", FontSize->14], StyleBox[", The first is the same as ", FontSize->14], StyleBox["Population", "Input", FontSize->14], StyleBox[" to start, while the second is empty (as shown by an empty pair \ of brackets.", FontSize->14] }], "Text"], Cell[BoxData[{ \(\(StillInLake\ = \ Population;\)\), "\[IndentingNewLine]", \(\(SecondCatch\ = \ {};\)\)}], "Input"], Cell[TextData[{ StyleBox["\tWe can use the ", FontSize->14], StyleBox["Length", "Input", FontSize->14], StyleBox[" function to determine how many elements each list, and therefore \ how many fish we have caught or are ", FontSize->14], StyleBox["StillInLake", "Input", FontSize->14], StyleBox[".", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Length[StillInLake]\)], "Input"], Cell[BoxData[ \(23\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tWe again choose a particular fish, this time from those ", FontSize->14], StyleBox["StillInLake", "Input", FontSize->14], StyleBox[". Notice that if the size of the list changes, so will the range \ of the ", FontSize->14], StyleBox["Random", "Input", FontSize->14], StyleBox[" numbers. We can then ", FontSize->14], StyleBox["Delete", "Input", FontSize->14], StyleBox[" the status of particular fish from those ", FontSize->14], StyleBox["StillInLake", "Input", FontSize->14], StyleBox[", and ", FontSize->14], StyleBox["Append", "Input", FontSize->14], StyleBox[" it to the ", FontSize->14], StyleBox["SecondCatch", "Input", FontSize->14], StyleBox["!", FontSize->14] }], "Text"], Cell[BoxData[{ \(\(CaughtThisOne\ = \ Random[Integer, {1, Length[StillInLake]}];\)\), "\[IndentingNewLine]", \(\(ThisFish\ = \ StillInLake[\([CaughtThisOne]\)];\)\), "\[IndentingNewLine]", \(\(StillInLake\ = \ Delete[StillInLake, CaughtThisOne];\)\), "\[IndentingNewLine]", \(\(SecondCatch\ = \ Append[SecondCatch, \ ThisFish];\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(StillInLake\)], "Input"], Cell[BoxData[ \({"Tagged", "Tagged", "Tagged", "Tagged", "Tagged", "Tagged", "Tagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged", "Untagged"}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SecondCatch\)], "Input"], Cell[BoxData[ \({"Untagged"}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tNow we simply ", FontSize->14], StyleBox["Do", "Input", FontSize->14], StyleBox[" this process over again until we have reached our\ntarget ", FontSize->14], StyleBox["NumSecondCatch", "Input", FontSize->14], StyleBox[". We put parentheses around the sequence to group it together \ inside a ", FontSize->14], StyleBox["Do", "Input", FontSize->14], StyleBox[" statement.", FontSize->14] }], "Text"], Cell[BoxData[{ \(\(PopSize\ = \ 23;\)\), "\[IndentingNewLine]", \(\(NumFirstCatch\ = \ 7;\)\), "\[IndentingNewLine]", \(\(NumSecondCatch\ = \ 12;\)\), "\[IndentingNewLine]", \(\(Population\ = \ Table["\", {PopSize}];\)\), "\[IndentingNewLine]", \(\(\(Do[\[IndentingNewLine]Population\ = \ ReplacePart[Population, "\", i], \[IndentingNewLine]{i, 1, NumFirstCatch}];\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(StillInLake\ = \ Population;\)\), "\[IndentingNewLine]", \(\(SecondCatch\ = \ {};\)\), "\[IndentingNewLine]", \(\(Do[\[IndentingNewLine]\((CaughtThisOne\ = \[IndentingNewLine]\t Random[Integer, {1, Length[StillInLake]}]; \[IndentingNewLine]ThisFish\ = \ StillInLake[\([CaughtThisOne]\)]; \[IndentingNewLine]StillInLake\ \ = \ Delete[StillInLake, CaughtThisOne]; \[IndentingNewLine]SecondCatch\ = \ Append[SecondCatch, \ ThisFish];)\), \[IndentingNewLine]{i, 1, NumSecondCatch}];\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(SecondCatch\)], "Input"], Cell[BoxData[ \({"Untagged", "Untagged", "Untagged", "Tagged", "Untagged", "Tagged", "Untagged", "Tagged", "Untagged", "Untagged", "Tagged", "Tagged"}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tThe number of fish ", FontSize->14], StyleBox["CaughtTwice", "Input", FontSize->14], StyleBox[" can then be easily determined using\n", FontSize->14], StyleBox["Count", "Input", FontSize->14], StyleBox[", which gives the number of elements in a list matching a certain \ value.", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(CaughtTwice\ = \ Count[SecondCatch, "\"]\)], "Input"], Cell[BoxData[ \(5\)], "Output"] }, Open ]], Cell[TextData[{ "\tIf the catch is truly random, probability says that the ratio of fish ", StyleBox["CaughtTwice", "Input"], " to the ", StyleBox["NumSecondCatch", "Input"], " should be the same as the ratio of the ", StyleBox["NumFirstCatch", "Input"], " tagged fish to the 'unknown' total population. Using our simulation, we \ should be able to make an estimate of the total population, ", StyleBox["PopEst", "Input"], " by solving for it in the ratio\n", StyleBox["\t", FontSize->14], StyleBox[Cell[BoxData[ \(TraditionalForm\`CaughtTwice\/NumSecondCatch = \ NumFirstCatch\/PopEst\)], "Input", FontSize->19], "Input"], "\n\t" }], "Text", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(PopEst\ = \ N[NumFirstCatch*NumSecondCatch/CaughtTwice]\)], "Input"], Cell[BoxData[ \(16.8`\)], "Output"] }, Open ]], Cell[TextData[{ "\tThe ", StyleBox["N[]", "Input"], " puts the output in number (not fractional) form. Notice that you can't do \ the division if ", StyleBox["CaughtTwice == 0", "Input"], ", i.e. you can't make an estimate unless you recapture at least one tagged \ fish! We can use an ", StyleBox["If[", "Input"], StyleBox["condition, truepart, falsepart", "Input", FontSlant->"Italic"], StyleBox["]", "Input"], " statement to return the value zero instead of doing the division, and \ thus avoid a possible error. The double equals (", StyleBox["==", "Input"], ") is used to make comparisons." }], "Text", FontSize->14], Cell[CellGroupData[{ Cell[BoxData[ \(PopEst\ = \ \[IndentingNewLine]If[\((CaughtTwice\ \[Equal] \ 0)\), \ \[IndentingNewLine]\ \ \ 0, \ \[IndentingNewLine]\ \ \ N[ NumFirstCatch* NumSecondCatch/CaughtTwice]\[IndentingNewLine]\ \ \ ]\)], "Input"], Cell[BoxData[ \(16.8`\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tHow good is the estimate? We can calculate a precentage error \ by comparing to ", FontSize->14], StyleBox["PopSize", "Input", FontSize->14], StyleBox[", which we already know. ", FontSize->14], StyleBox["Abs[]", "Input", FontSize->14], StyleBox[" is the absolute value function.", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(PctErr\ = \ N[Abs[PopSize\ - \ PopEst]/PopSize*100]\)], "Input"], Cell[BoxData[ \(26.95652173913043`\)], "Output"] }, Open ]], Cell[TextData[StyleBox["\tThe error will range between 8.7 percent and 265 \ percent, although values from 8.7 to 30 percent are most likely. Notice, \ however, that we caught over half of the fish in the pond as part of the \ recapture, which, although really helpful for our accuracy, is probably not a \ reasonable sample size!", FontSize->14]], "Text"], Cell[TextData[{ StyleBox["\tPutting it all together, we have a small set of commands with \ the ", FontSize->14], StyleBox["parameters", FontSize->14, FontSlant->"Italic"], StyleBox[" listed first, where we can easily find and adjust them, and \ where the final statement is a list of outputs, which include the estimate \ for the population, the actual population size, and the computed percentage \ error. Let's see what we get with a population of 200 and catch and recatch \ both of 50:", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(PopSize\ = 200;\)\), "\[IndentingNewLine]", \(\(NumFirstCatch\ = \ 50;\)\), "\[IndentingNewLine]", \(\(NumSecondCatch\ = \ 50;\)\), "\[IndentingNewLine]", \(\(Population\ = \ Table["\", {PopSize}];\)\), "\[IndentingNewLine]", \(\(Do[\[IndentingNewLine]Population\ = \ ReplacePart[Population, "\", i], \[IndentingNewLine]{i, 1, NumFirstCatch}];\)\), "\[IndentingNewLine]", \(\(StillInLake\ = \ Population;\)\), "\[IndentingNewLine]", \(\(SecondCatch\ = \ {};\)\), "\[IndentingNewLine]", \(\(Do[\[IndentingNewLine]\((CaughtThisOne\ = \[IndentingNewLine]\t Random[Integer, {1, Length[StillInLake]}]; \[IndentingNewLine]ThisFish\ = \ StillInLake[\([CaughtThisOne]\)]; \[IndentingNewLine]StillInLake\ \ = \ Delete[StillInLake, CaughtThisOne]; \[IndentingNewLine]SecondCatch\ = \ Append[SecondCatch, \ ThisFish];)\), \[IndentingNewLine]{i, 1, NumSecondCatch}];\)\), "\[IndentingNewLine]", \(\(CaughtTwice\ = \ Count[SecondCatch, "\"];\)\), "\[IndentingNewLine]", \(\(PopEst\ = If[\((CaughtTwice\ \[Equal] \ 0)\), \ 0, \ \[IndentingNewLine]N[ NumFirstCatch* NumSecondCatch/CaughtTwice]]\ ;\)\), "\[IndentingNewLine]", \(\(PctErr\ = \ N[Abs[PopSize\ - \ PopEst]/ PopSize*100];\)\), "\[IndentingNewLine]", \(\(\({PopEst, PopSize, PctErr}\)\(\[IndentingNewLine]\) \)\)}], "Input"], Cell[BoxData[ \({208.33333333333334`, 200, 4.166666666666671`}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tIf we have a sequence of statements with clear inputs and \ outputs, it is often useful to define the group as a ", FontSize->14], StyleBox["function", FontSize->14, FontSlant->"Italic"], StyleBox[". We will call our function ", FontSize->14], StyleBox["GuessPop", "Input", FontSize->14], StyleBox[" and require three inputs: the actual population size and the \ size of each catch. We use the trailing underline to designate a variable as \ an ", FontSize->14], StyleBox["input parameter", FontSize->14, FontSlant->"Italic"], StyleBox[", and use the ': =\" to tell ", FontSize->14], StyleBox["Mathematica", FontSize->14, FontSlant->"Italic"], StyleBox[" to 'evaluate later' (i.e. when the function is called with given \ inputs). We group the statements in the function with parentheses,\n", FontSize->14] }], "Text"], Cell[BoxData[ \(GuessPop[PopSize_, NumFirstCatch_, NumSecondCatch_]\ := \ \ \[IndentingNewLine]\((\[IndentingNewLine]Population\ = \ Table["\", {PopSize}]; \[IndentingNewLine]Do[\ \[IndentingNewLine]Population\ = \ ReplacePart[Population, "\", i], \[IndentingNewLine]{i, 1, NumFirstCatch}]; \[IndentingNewLine]StillInLake\ = \ Population; \[IndentingNewLine]SecondCatch\ = \ {}; \ \[IndentingNewLine]Do[\[IndentingNewLine]\((CaughtThisOne\ = \ \[IndentingNewLine]\t Random[Integer, {1, Length[StillInLake]}]; \[IndentingNewLine]ThisFish\ = \ StillInLake[\([CaughtThisOne]\)]; \ \[IndentingNewLine]StillInLake\ = \ Delete[StillInLake, CaughtThisOne]; \[IndentingNewLine]SecondCatch\ = \ Append[SecondCatch, \ ThisFish];)\), \[IndentingNewLine]{i, 1, NumSecondCatch}]; \[IndentingNewLine]CaughtTwice\ = \ Count[SecondCatch, "\"]; \[IndentingNewLine]PopEst\ = If[\((CaughtTwice\ \[Equal] \ 0)\), \ 0, \ \[IndentingNewLine]N[ NumFirstCatch* NumSecondCatch/ CaughtTwice]]\ ; \[IndentingNewLine]PctErr\ = \ N[Abs[PopSize\ - \ PopEst]/ PopSize*100]; \[IndentingNewLine]{PopEst, PopSize, PctErr}\[IndentingNewLine])\)\)], "Input"], Cell[TextData[StyleBox["\tNow we can put population and catch numbers \ directly into our new function!", FontSize->14]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(GuessPop[23, 7, 12]\)], "Input"], Cell[BoxData[ \({21.`, 23, 8.695652173913043`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(GuessPop[200, 50, 50]\)], "Input"], Cell[BoxData[ \({227.27272727272728`, 200, 13.63636363636364`}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tSo, how many fish do you need to tag and/or recatch to get a \ 'good' population guess? Because we now have a model, we can explore what \ happens relatively easily! Let's start with a medium sized population, say \ 150 fish, and catch and tag 20 percent, or 30 of those fish. If we don't \ catch ", FontSize->14], StyleBox["any", FontSize->14, FontWeight->"Bold"], StyleBox[" fish in the second catch, we will catch zero tagged fish, and \ predict zero fish in the pond, which is 100 percent error. ", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(GuessPop[150, 30, 0]\)], "Input"], Cell[BoxData[ \({0, 150, 100.`}\)], "Output"] }, Open ]], Cell[TextData[StyleBox["\tOn the other end, if we catch 150 fish in the \ second catch (all of them!), we will catch all 30 tagged fish, and our \ estimate will be perfect (0 percent error).", FontSize->14]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(GuessPop[150, 30, 150]\)], "Input"], Cell[BoxData[ \({150.`, 150, 0.`}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tTo see what happens in between, we can simply look at results \ for second catches from 1 to 149. Just like the ", FontSize->14], StyleBox["Do", "Input", FontSize->14], StyleBox[" function, the ", FontSize->14], StyleBox["Table", "Input", FontSize->14], StyleBox[" function can also include a ", FontSize->14], StyleBox["counter", FontSize->14, FontSlant->"Italic"], StyleBox[" (often a single letter variable) that can be used to determine \ each value in the list that ", FontSize->14], StyleBox["Table", "Input", FontSize->14], StyleBox[" creates. For example, to generate an '11 times table', we could \ evaluate", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Table[11*i, {i, 12}]\)], "Input"], Cell[BoxData[ \({11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tTo create a list of population guesses for second catches from \ 1 to 150, we can make a ", FontSize->14], StyleBox["Table", "Input", FontSize->14], StyleBox[" of the first part (", FontSize->14], StyleBox["[[1]]", "Input", FontSize->14], StyleBox[") of each of ", FontSize->14], StyleBox["i", "Input", FontSize->14], StyleBox[" guesses (remember, ", FontSize->14], StyleBox["GuessPop", "Input", FontSize->14], StyleBox[" returns three parts!), where ", FontSize->14], StyleBox["i", "Input", FontSize->14], StyleBox[" goes from 1 to ", FontSize->14], StyleBox["PopSize", "Input", FontSize->14], StyleBox[" (= 150). We give the list a name (", FontSize->14], StyleBox["Est2Catch", "Input", FontSize->14], StyleBox[") and we use the semicolon to make sure the list doesn't output \ (because it is 150 numbers long!). We can make a similar list of the \ percentage errors, which come from part three (", FontSize->14], StyleBox["[[3]]", "Input", FontSize->14], StyleBox[") and we label ", FontSize->14], StyleBox["Err2Catch", "Input", FontSize->14], StyleBox[". Note that this might take some computational time!", FontSize->14] }], "Text"], Cell[BoxData[{ \(\(PopSize\ = \ 150;\)\), "\[IndentingNewLine]", \(\(Est2Catch\ = \[IndentingNewLine]Table[\(GuessPop[PopSize, 30, i]\)[\([1]\)], {i, PopSize}];\)\), "\[IndentingNewLine]", \(\(Err2Catch\ = \[IndentingNewLine]Table[\(GuessPop[PopSize, 30, i]\)[\([3]\)], {i, PopSize}];\)\)}], "Input"], Cell[TextData[{ StyleBox["\tTo ", FontSize->14], StyleBox["visualize", FontSize->14, FontSlant->"Italic"], StyleBox[" our results, we can plot the data from each list using ", FontSize->14], StyleBox["ListPlot", "Input", FontSize->14], StyleBox[". We store each graph by giving it a name. Each plot is a graph \ of the ", FontSize->14], StyleBox["position in the list", FontSize->14, FontSlant->"Italic"], StyleBox[" on the x-axis (which in this case corresponds to number in the \ second catch) and the ", FontSize->14], StyleBox["value of list elements", FontSize->14, FontSlant->"Italic"], StyleBox[" on the y-axis (corresponding here to the estimated population \ for the first graph and the percent error for the second).", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(PlotEst\ = \ ListPlot[Est2Catch, PlotRange \[Rule] {0, 2*PopSize}];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 -2.60209e-017 0.00206011 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .10301 -12 -4.5 ] [.01131 .10301 0 4.5 ] [.01131 .20601 -18 -4.5 ] [.01131 .20601 0 4.5 ] [.01131 .30902 -18 -4.5 ] [.01131 .30902 0 4.5 ] [.01131 .41202 -18 -4.5 ] [.01131 .41202 0 4.5 ] [.01131 .51503 -18 -4.5 ] [.01131 .51503 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .10301 m .03006 .10301 L s [(50)] .01131 .10301 1 0 Mshowa .02381 .20601 m .03006 .20601 L s [(100)] .01131 .20601 1 0 Mshowa .02381 .30902 m .03006 .30902 L s [(150)] .01131 .30902 1 0 Mshowa .02381 .41202 m .03006 .41202 L s [(200)] .01131 .41202 1 0 Mshowa .02381 .51503 m .03006 .51503 L s [(250)] .01131 .51503 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(300)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0206 m .02756 .0206 L s .02381 .0412 m .02756 .0412 L s .02381 .0618 m .02756 .0618 L s .02381 .0824 m .02756 .0824 L s .02381 .12361 m .02756 .12361 L s .02381 .14421 m .02756 .14421 L s .02381 .16481 m .02756 .16481 L s .02381 .18541 m .02756 .18541 L s .02381 .22661 m .02756 .22661 L s .02381 .24721 m .02756 .24721 L s .02381 .26781 m .02756 .26781 L s .02381 .28842 m .02756 .28842 L s .02381 .32962 m .02756 .32962 L s .02381 .35022 m .02756 .35022 L s .02381 .37082 m .02756 .37082 L s .02381 .39142 m .02756 .39142 L s .02381 .43262 m .02756 .43262 L s .02381 .45322 m .02756 .45322 L s .02381 .47383 m .02756 .47383 L s .02381 .49443 m .02756 .49443 L s .02381 .53563 m .02756 .53563 L s .02381 .55623 m .02756 .55623 L s .02381 .57683 m .02756 .57683 L s .02381 .59743 m .02756 .59743 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 .0618 Mdot .03651 0 Mdot .04286 0 Mdot .04921 0 Mdot .05556 0 Mdot .0619 .18541 Mdot .06825 .43262 Mdot .0746 .12361 Mdot .08095 .27812 Mdot .0873 .30902 Mdot .09365 .33992 Mdot .10635 .40172 Mdot .1127 .17305 Mdot .11905 .23176 Mdot .1254 .49443 Mdot .13175 .21013 Mdot .1381 .15892 Mdot .14444 .39142 Mdot .15079 .17658 Mdot .15714 .16223 Mdot .16984 .2843 Mdot .17619 .37082 Mdot .18254 .30902 Mdot .18889 .53563 Mdot .19524 .55623 Mdot .20159 .24721 Mdot .20794 .59743 Mdot .21429 .23176 Mdot .22063 .2737 Mdot .22698 .32962 Mdot .23333 .33992 Mdot .23968 .26266 Mdot .24603 .43262 Mdot .25238 .31785 Mdot .25873 .38112 Mdot .26508 .58713 Mdot .27143 .34433 Mdot .27778 .27468 Mdot .29048 .25957 Mdot .29683 .26575 Mdot .30317 .20918 Mdot .30952 .25283 Mdot .31587 .2843 Mdot .32222 .20748 Mdot .32857 .29666 Mdot .33492 .33649 Mdot .34127 .38627 Mdot .34762 .24246 Mdot .35397 .24721 Mdot .36032 .36395 Mdot .36667 .22249 Mdot .37302 .30902 Mdot .37937 .31464 Mdot .38571 .35228 Mdot .39206 .27574 Mdot .39841 .28049 Mdot .40476 .37082 Mdot .41111 .25133 Mdot .41746 .2737 Mdot .42381 .25957 Mdot .43016 .28253 Mdot .43651 .50215 Mdot .44921 .37644 Mdot .45556 .28018 Mdot .4619 .26653 Mdot .46825 .28842 Mdot .4746 .29254 Mdot .48095 .37082 Mdot .4873 .25065 Mdot .49365 .28584 Mdot .5 .2897 Mdot .50635 .39142 Mdot .5127 .39657 Mdot .51905 .40172 Mdot .5254 .2872 Mdot .53175 .49443 Mdot .5381 .31288 Mdot .54444 .26673 Mdot .55079 .32061 Mdot .55714 .43262 Mdot .56349 .30902 Mdot .56984 .29528 Mdot .57619 .33606 Mdot .58254 .27193 Mdot .58889 .26193 Mdot .59524 .32719 Mdot .60159 .37494 Mdot .60794 .37906 Mdot .61429 .28739 Mdot .62063 .30576 Mdot .62698 .34537 Mdot .63333 .29666 Mdot .63968 .28547 Mdot .64603 .31878 Mdot .65238 .38241 Mdot .65873 .32528 Mdot .66508 .36718 Mdot .67143 .3152 Mdot .67778 .33504 Mdot .68413 .35709 Mdot .69048 .28215 Mdot .69683 .36395 Mdot .70317 .34805 Mdot .70952 .31785 Mdot .71587 .2591 Mdot .72222 .29558 Mdot .72857 .31183 Mdot .73492 .30096 Mdot .74127 .31744 Mdot .74762 .30633 Mdot .75397 .27336 Mdot .76032 .29872 Mdot .76667 .36155 Mdot .77302 .31708 Mdot .77937 .3343 Mdot .78571 .30902 Mdot .79206 .31159 Mdot .79841 .3016 Mdot .80476 .31674 Mdot .81111 .28384 Mdot .81746 .28613 Mdot .82381 .31149 Mdot .83016 .32704 Mdot .83651 .30426 Mdot .84286 .28474 Mdot .84921 .30902 Mdot .85556 .32385 Mdot .8619 .28131 Mdot .86825 .30444 Mdot .8746 .34507 Mdot .88095 .30902 Mdot .8873 .31131 Mdot .89365 .33868 Mdot .9 .31588 Mdot .90635 .29623 Mdot .9127 .29836 Mdot .91905 .31122 Mdot .9254 .31343 Mdot .93175 .33992 Mdot .9381 .29666 Mdot .94444 .32005 Mdot .95079 .31115 Mdot .95714 .30284 Mdot .96349 .31541 Mdot .96984 .30696 Mdot .97619 .30902 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooo00<0003oooooool00_ooo`040000oooooooo00001?ooo`030000oooooooo 0?ooool3oooo000>oooo0`0000?oool200001Oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool02_ooo`030000oooooooo0?Goool001_oool200002oooo`030000oooooooo0?Goool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?oo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool0 0`000?ooooooo`0Joooo00<0003oooooool0iOooo`006oooo`030000oooooooo01[oool00`000?oo ooooo`02oooo00<0003oooooool0h?ooo`006oooo`030000oooooooo01ooool00`000?ooooooo`3P oooo000Koooo0P000?ooool4oooo000Koooo00<0003oooooool05?ooo`030000oooooooo0>_oool0 01_oool00`000?ooooooo`0Doooo00<0003oooooool01oooo`030000oooooooo0>7oool001_oool0 0`000?ooooooo`0Noooo00<0003oooooool0hOooo`006oooo`030000oooooooo00Koool00`000?oo ooooo`3ioooo000Koooo0P0000Ooool00`000?ooooooo`3ioooo000Koooo00<0003oooooool0oooo o`?oool001_oool00`000?ooooooo`3ooooo0oooo`001oooo`D00002oooo0P0000Coool200001Ooo o`030000oooooooo0?ooool3oooo0009oooo00D0003oooooooooool000000_ooo`040000oooooooo 00000_ooo`030000oooooooo00;oool00`000?ooooooo`3ooooo0oooo`002Oooo`050000oooooooo oooo000000;oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo0`0004[oool00`000?oo ooooo`2eoooo0009oooo00D0003oooooooooool000000_ooo`040000oooooooo00000_ooo`030000 oooooooo00;oool00`000?ooooooo`0Ioooo00<0003oooooool0:Oooo`030000oooooooo00;oool0 0`000?ooooooo`2eoooo0009oooo00D0003oooooooooool000000_ooo`040000oooooooo00000_oo o`030000oooooooo00;oool00`000?ooooooo`0Ioooo00<0003oooooool0:Oooo`030000oooooooo 0;[oool000Soool200001?ooo`800004oooo0P0000Goool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo05Goool00`000?ooooooo`2Zoooo000Koooo00<0003oooooool0EOooo`030000 oooooooo0:[oool001_oool200005_ooo`030000oooooooo01Koool00`000?ooooooo`3Aoooo000K oooo00<0003oooooool05Oooo`030000oooooooo01Koool00`000?ooooooo`3Aoooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`1Aoooo00<0003oooooool0[_ooo`006ooo o`030000oooooooo02_oool00`000?ooooooo`0Soooo0P000:ooool001_oool20000;?ooo`030000 oooooooo02Coool00`000?ooooooo`0oooo00<0003oooooool0>Oooo`030000oooooooo02[oool0 0`000?ooooooo`0Yoooo000Koooo00<0003oooooool08_ooo`030000oooooooo02?oool00`000?oo ooooo`0Coooo00<0003oooooool01Oooo`030000oooooooo00Coool00`000?ooooooo`06oooo00<0 003oooooool08oooo`030000oooooooo00[oool00`000?ooooooo`0Moooo0P0000Koool00`000?oo ooooo`02oooo00<0003oooooool0:Oooo`006oooo`030000oooooooo02;oool00`000?ooooooo`0S oooo00<0003oooooool06oooo`030000oooooooo00Ooool00`000?ooooooo`03oooo00<0003oool0 00001_ooo`030000oooooooo01Coool00`000?ooooooo`03oooo00<0003oooooool0:_ooo`800006 oooo00<0003oooooool0;_ooo`006oooo`80001aoooo0P0000Koool00`000?ooooooo`04oooo00<0 003oooooool05?ooo`030000oooooooo06Woool001_oool00`000?ooooooo`1oooo00<0003oooooool05?ooo`030000 oooooooo02coool00`000?ooooooo`06oooo00<0003oooooool05Oooo`006oooo`030000oooooooo 04coool00`000?ooooooo`0koooo00<0003oooooool03_ooo`030000oooooooo01Coool010000?oo ooooo`0000Koool00`000?ooooooo`06oooo00<0003oooooool06Oooo`030000oooo000000Koool0 0`000?ooooooo`0Eoooo0007oooo1@0000;oool200001?ooo`800005oooo00<0003oooooool0]Ooo o`030000oooooooo00Coool00`000?ooooooo`06oooo00<0003oooooool01oooo`030000oooooooo 00Goool00`000?ooooooo`09oooo00<0003oooooool02Oooo`030000oooooooo013oool000Woool0 1@000?ooooooooooo`000002oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`030000 oooooooo00goool00`000?ooooooo`0Foooo00<0003oooooool0;_ooo`030000oooooooo02koool0 0`000?ooooooo`0?ooo`030000oooooooo04[oool00`000?ooooooo`0Foooo00<0003oooooool03Oooo`030000 oooooooo00Koool00`000?ooooooo`0Joooo00<0003oooooool05?ooo`030000oooooooo01Coool0 01_oool00`000?ooooooo`2Aoooo00<0003oooooool03Oooo`030000oooooooo02[oool00`000?oo ooooo`03oooo00<0003oooooool0:oooo`006oooo`80000boooo00<0003oooooool0GOooo`030000 oooooooo00goool00`000?ooooooo`0Zoooo00<0003oooooool0?ooo`030000oooooooo017oool00`000?ooooooo`0Loooo00<0 003oooooool0KOooo`006oooo`030000oooooooo06_oool00`000?ooooooo`0Toooo00<0003ooooo ool0KOooo`006oooo`030000oooooooo03Woool00`000?ooooooo`0_oooo00<0003oooooool09_oo o`030000oooooooo00Woool00`000?ooooooo`1Ooooo000Koooo00<0003oooooool0>Oooo`030000 oooooooo01?oool00`000?ooooooo`12oooo00<0003oooooool02Oooo`030000oooooooo05ooool0 01_oool00`000?ooooooo`1?oooo00<0003oooooool0/?ooo`006oooo`80000Moooo00<0003ooooo ool0Foooo`030000oooooooo08Goool001_oool00`000?ooooooo`0Loooo00<0003oooooool0Fooo o`800026oooo000Koooo00<0003oooooool04_ooo`030000oooooooo06Koool00`000?ooo`000024 oooo000Koooo00<0003oooooool04_ooo`030000oooooooo06Soool00`000?ooooooo`22oooo0007 oooo100000?oool200001?ooo`800005oooo00<0003oooooool0ooooo`?oool000Ooool00`000?oo ooooo`03oooo00@0003oooooool00002oooo00@0003oooooool00004oooo00<0003oooooool0oooo o`?oool000Soool00`000?ooooooo`02oooo00@0003oooooool00002oooo00@0003oooooool00004 oooo0`000?ooool3oooo0009oooo00D0003oooooooooool000000_ooo`040000oooooooo00000_oo o`030000oooooooo00;oool00`000?ooooooo`3ooooo0oooo`001oooo`040000oooooooo00000_oo o`040000oooooooo00000_ooo`040000oooooooo00001?ooo`030000oooooooo0?ooool3oooo0008 oooo0P0000Coool200001?ooo`800005oooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`08oooo00<0003oooooool0:oooo`030000oooooooo04koool00`000?ooooooo`1hoooo000K oooo0P0000Woool00`000?ooooooo`0[oooo00<0003oooooool0C_ooo`030000oooooooo07Soool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?oo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool20000ooooo`Coool001_oool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`0Goooo00<0003oooooool0I_ooo`030000oooooooo07ooool001_oool200006?ooo`030000 oooooooo06Koool00`000?ooooooo`1ooooo000Koooo00<0003oooooool0J?ooo`030000oooooooo 09Ooool001_oool00`000?ooooooo`1Xoooo00<0003oooooool0Uoooo`001oooo`@00003oooo0P00 00Coool200001Oooo`030000oooooooo0?ooool3oooo0007oooo00<0003oooooool00oooo`040000 oooooooo00000_ooo`040000oooooooo00001?ooo`030000oooooooo0?ooool3oooo0008oooo00<0 003oooooool01Oooo`040000oooooooo00000_ooo`030000oooooooo00;oool30000ooooo`?oool0 00Woool00`000?ooooooo`02oooo0P0000?oool010000?ooooooo`0000Coool00`000?ooooooo`3o oooo0oooo`001oooo`040000oooooooo00000oooo`030000oooooooo00;oool010000?ooooooo`00 00Coool00`000?ooooooo`3ooooo0oooo`002?ooo`800004oooo0`0000?oool200001Oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`0W oooo00<0003oooooool0f?ooo`006oooo`80000Xoooo00<0003oooooool0f?ooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo02Woool00`000?ooooooo`3Foooo000Koooo0P0002[oool0 0`000?ooooooo`3Foooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool20000ooooo`Coool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 03_oool00`000?ooooooo`34oooo000Koooo00<0003oooooool0>oooo`030000oooooooo0"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -22.9235, \ 0.607629, 1.8727}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(PlotErr\ = \ ListPlot[Err2Catch, PlotRange \[Rule] {0, 100}];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 1.73472e-017 0.00618034 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .12361 -12 -4.5 ] [.01131 .12361 0 4.5 ] [.01131 .24721 -12 -4.5 ] [.01131 .24721 0 4.5 ] [.01131 .37082 -12 -4.5 ] [.01131 .37082 0 4.5 ] [.01131 .49443 -12 -4.5 ] [.01131 .49443 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .12361 m .03006 .12361 L s [(20)] .01131 .12361 1 0 Mshowa .02381 .24721 m .03006 .24721 L s [(40)] .01131 .24721 1 0 Mshowa .02381 .37082 m .03006 .37082 L s [(60)] .01131 .37082 1 0 Mshowa .02381 .49443 m .03006 .49443 L s [(80)] .01131 .49443 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(100)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0309 m .02756 .0309 L s .02381 .0618 m .02756 .0618 L s .02381 .09271 m .02756 .09271 L s .02381 .15451 m .02756 .15451 L s .02381 .18541 m .02756 .18541 L s .02381 .21631 m .02756 .21631 L s .02381 .27812 m .02756 .27812 L s .02381 .30902 m .02756 .30902 L s .02381 .33992 m .02756 .33992 L s .02381 .40172 m .02756 .40172 L s .02381 .43262 m .02756 .43262 L s .02381 .46353 m .02756 .46353 L s .02381 .52533 m .02756 .52533 L s .02381 .55623 m .02756 .55623 L s .02381 .58713 m .02756 .58713 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 .61803 Mdot .03651 .61803 Mdot .04286 .61803 Mdot .04921 .12361 Mdot .05556 .61803 Mdot .0619 .12361 Mdot .06825 .24721 Mdot .0746 .12361 Mdot .08095 .49443 Mdot .0873 .30902 Mdot .1 .12361 Mdot .10635 .18541 Mdot .1127 .24721 Mdot .11905 .15451 Mdot .13175 .09271 Mdot .1381 .17305 Mdot .14444 .14833 Mdot .15079 .61803 Mdot .16349 .07416 Mdot .17619 .02472 Mdot .18254 .10301 Mdot .18889 .18541 Mdot .19524 .49443 Mdot .20159 .07416 Mdot .20794 .27812 Mdot .21429 .08829 Mdot .22063 .07063 Mdot .22698 .05297 Mdot .23333 .03532 Mdot .23968 .19777 Mdot .24603 .10301 Mdot .25238 .24721 Mdot .25873 .52533 Mdot .26508 .0309 Mdot .27143 .0824 Mdot .27778 .06867 Mdot .28413 .11125 Mdot .29048 .42026 Mdot .29683 .08652 Mdot .30317 .07416 Mdot .30952 0 Mdot .31587 .19424 Mdot .32222 .03708 Mdot .32857 .56859 Mdot .33492 .24721 Mdot .34127 .06867 Mdot .34762 .04495 Mdot .35397 .09614 Mdot .36032 .31785 Mdot .36667 .0618 Mdot .37302 .13734 Mdot .37937 .0412 Mdot .38571 .14833 Mdot .39206 .0206 Mdot .39841 .11125 Mdot .40476 .20601 Mdot .41111 .06742 Mdot .41746 .0206 Mdot .42381 .18541 Mdot .43016 .09064 Mdot .43651 0 Mdot .44286 .0618 Mdot .44921 .21013 Mdot .45556 .22249 Mdot .4619 .15732 Mdot .46825 .07725 Mdot .4746 .05705 Mdot .48095 .0618 Mdot .4873 .20227 Mdot .49365 .00824 Mdot .5 0 Mdot .50635 .10459 Mdot .5127 .08927 Mdot .51905 .1106 Mdot .5254 .07946 Mdot .53175 .08829 Mdot .5381 .0618 Mdot .54444 .13538 Mdot .55079 .04807 Mdot .55714 .00727 Mdot .56349 .0824 Mdot .56984 .11183 Mdot .57619 .10595 Mdot .58254 .07416 Mdot .58889 .00687 Mdot .59524 .03635 Mdot .60159 .05562 Mdot .60794 .14009 Mdot .61429 .05817 Mdot .62063 .00651 Mdot .62698 .07271 Mdot .63333 .05297 Mdot .63968 .04709 Mdot .64603 .09452 Mdot .65238 .02602 Mdot .65873 .02943 Mdot .66508 .05057 Mdot .67143 .04554 Mdot .67778 .03933 Mdot .68413 .05855 Mdot .69048 .0309 Mdot .69683 .04837 Mdot .70317 .06695 Mdot .70952 .01124 Mdot .71587 .05665 Mdot .72222 .13734 Mdot .72857 .0215 Mdot .73492 .0412 Mdot .74127 .01075 Mdot .74762 .02247 Mdot .75397 0 Mdot .76032 .09889 Mdot .76667 .03933 Mdot .77302 .04495 Mdot .77937 .02967 Mdot .78571 .02687 Mdot .79206 .01978 Mdot .79841 .01483 Mdot .80476 .07304 Mdot .81111 .11183 Mdot .81746 .05374 Mdot .82381 .00494 Mdot .83016 .01426 Mdot .83651 .0412 Mdot .84286 .00475 Mdot .84921 .04415 Mdot .85556 .05665 Mdot .8619 .09136 Mdot .86825 .06695 Mdot .8746 .00458 Mdot .88095 .07725 Mdot .8873 .01766 Mdot .89365 .0341 Mdot .9 .02984 Mdot .90635 .00441 Mdot .9127 .02289 Mdot .91905 .01705 Mdot .9254 .01279 Mdot .93175 .02884 Mdot .9381 .02472 Mdot .94444 0 Mdot .95079 .01648 Mdot .95714 .01236 Mdot .96349 .00824 Mdot .96984 .00412 Mdot .97619 0 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooo00<0003oooooool01oooo`030000oooooooo 00goool01@000?ooooooooooo`00000^oooo000Koooo00<0003oooooool0DOooo`030000oooooooo 037oool00`000?ooooooo`0Doooo00<0003oooooool01?ooo`800006oooo00<0003oooooool04Ooo o`030000oooooooo017oool00`000?ooooooo`0/oooo000Koooo00<0003oooooool0oooo00<0003oooooool03Oooo`050000oooooooooooo0000017oool00`000?ooooooo`05 oooo00<0003oooooool08Oooo`030000oooooooo02_oool001_oool20000E_ooo`030000oooooooo 017oool00`000?ooooooo`07oooo00<0003oooooool03?ooo`030000oooooooo07goool001_oool0 0`000?ooooooo`0noooo00<0003oooooool03_ooo`030000oooooooo00ooool00`000?ooooooo`19 oooo00<0003oooooool09oooo`030000oooooooo02Soool001_oool00`000?ooooooo`0`oooo00<0 003oooooool02oooo`030000oooooooo00koool00`000?ooooooo`0?oooo00<0003oooooool0=Ooo o`030000oooooooo017oool00`000?ooooooo`0Goooo00<0003oooooool03Oooo`030000oooooooo 02Soool001_oool00`000?ooooooo`0Qoooo00<0003oooooool01oooo`030000oooooooo00;oool0 0`000?ooooooo`0Boooo00<0003oooooool0:?ooo`030000oooooooo01[oool00`000?ooooooo`09 oooo00<0003oooooool0:oooo`030000oooooooo017oool00`000?ooooooo`0Toooo000Koooo00<0 003oooooool08Oooo`030000oooooooo00Ooool00`000?ooooooo`0Goooo00<0003oooooool0:?oo o`030000oooooooo00coool00`000?ooooooo`0;oooo00<0003oooooool0Boooo`030000oooooooo 02Coool001_oool00`000?ooooooo`0moooo00<0003oooooool0?oooo`030000oooooooo00Koool0 0`000?ooooooo`1goooo000Koooo00<0003oooooool0;_ooo`030000oooooooo00coool00`000?oo ooooo`03oooo00<0003oooooool0=Oooo`030000oooooooo00;oool00`000?ooooooo`05oooo00<0 003oooooool0Moooo`006oooo`030000oooooooo01Woool00`000?ooooooo`0Boooo00<0003ooooo ool04_ooo`030000oooooooo023oool00`000?ooooooo`0Boooo00<0003oooooool00_ooo`030000 oooooooo05?oool00`000?ooooooo`0Yoooo000Koooo0P0001[oool00`000?ooooooo`0foooo00<0 003oooooool04Oooo`030000oooooooo03Goool00`000?ooooooo`0eoooo00<0003oooooool0:Ooo o`006oooo`030000oooooooo05;oool00`000?ooooooo`19oooo00<0003oooooool06oooo`030000 oooooooo04?oool001_oool00`000?ooooooo`0Voooo00<0003oooooool03Oooo`030000oooooooo 047oool00`000?ooooooo`0ooooo00<0003oooooool0@oooo`006oooo`030000oooooooo02Koool0 0`000?ooooooo`0=oooo00<0003oooooool0@Oooo`030000oooooooo00ooool00`000?ooooooo`1c oooo000Koooo00<0003oooooool0@?ooo`030000oooooooo01_oool00`000?ooooooo`0Loooo00<0 003oooooool02_ooo`030000oooo000003coool00`000?ooooooo`0foooo000Koooo00<0003ooooo ool0@?ooo`030000oooooooo01_oool00`000?ooooooo`0Loooo00<0003oooooool02_ooo`030000 oooooooo03coool00`000?ooooooo`0foooo000=oooo100000?oool200001Oooo`030000oooooooo 0?ooool3oooo000=oooo00<0003oooooool00oooo`040000oooooooo00001?ooo`030000oooooooo 00?oool010000?ooooooo`0000?oool00`000?ooooooo`03oooo00<0003oooooool0koooo`003_oo o`030000oooooooo00;oool010000?ooooooo`0000Coool300000oooo`040000oooooooo00000ooo o`030000oooooooo00?oool00`000?ooooooo`3_oooo000?oooo00D0003oooooooooool000000_oo o`030000oooooooo00;oool00`000?ooooooo`3ooooo0oooo`003Oooo`040000oooooooo00000_oo o`040000oooooooo00001?ooo`030000oooooooo08Coool00`000?ooooooo`1koooo000>oooo0P00 00Coool200001Oooo`030000oooooooo05Ooool00`000?ooooooo`0Zoooo00<0003oooooool0:ooo o`030000oooooooo04goool001_oool00`000?ooooooo`1Goooo00<0003oooooool0>_ooo`030000 oooooooo01_oool00`000?ooooooo`1=oooo000Koooo00<0003oooooool0U?ooo`030000oooooooo 06_oool001_oool00`000?ooooooo`0Loooo00<0003oooooool0>oooo`030000oooooooo0:Goool0 01_oool00`000?ooooooo`0Eoooo00<0003oooooool01?ooo`030000oooooooo03_oool00`000?oo ooooo`2Uoooo000Koooo0P0001Koool00`000?ooooooo`1Foooo00<0003oooooool0TOooo`006ooo o`030000oooooooo06koool00`000?ooooooo`2Aoooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo01[oool00`000?ooooooo`3U oooo000Koooo00<0003oooooool06_ooo`030000oooooooo0>Goool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo01;oool00`000?ooooooo`0Boooo00<0003oooooool0>_oo o`030000oooooooo09_oool001_oool200004oooo`030000oooooooo01;oool00`000?ooooooo`0j oooo00<0003oooooool0Voooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0B?ooo`030000oooooooo0;Ooool001_oool00`000?ooooooo`0eoooo00<0003oooooool04?oo o`030000oooooooo0;Ooool001_oool00`000?ooooooo`0eoooo00<0003oooooool0?Oooo`030000 oooooooo08[oool001_oool00`000?ooooooo`1Ooooo00<0003oooooool04oooo`030000oooooooo 08[oool001_oool00`000?ooooooo`1Ooooo00<0003oooooool02Oooo`030000oooooooo09Coool0 01_oool00`000?ooooooo`1[oooo00<0003oooooool0U?ooo`006oooo`80003ooooo1?ooo`006ooo o`030000oooooooo06goool00`000?ooooooo`2Boooo000Koooo00<0003oooooool0KOooo`030000 oooooooo09;oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool0ooooo`?oool000ooool300000_ooo`800005oooo00<0003ooooo ool0ooooo`?oool0013oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0003ooooo ool02?ooo`030000oooooooo00Woool00`000?ooooooo`0Qoooo00<0003oooooool04_ooo`030000 oooooooo0;;oool000goool5000000Goool0003oooooool000001?ooo`<00008oooo00<0003ooooo ool02Oooo`030000oooooooo027oool00`000?ooooooo`0Boooo00<0003oooooool0/_ooo`003Ooo o`040000oooooooo00000_ooo`040000oooooooo00001?ooo`030000oooooooo0?ooool3oooo000> oooo00<0003oool000000_ooo`040000oooooooo00001?ooo`030000oooooooo0?ooool3oooo000? oooo0P0000?oool200001Oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0oooo o`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0;?ooo`030000oooooooo0=?oool001_oool20000;Oooo`030000oooooooo 0=?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`0= oooo00<0003oooooool0l_ooo`006oooo`80000>oooo00<0003oooooool0l_ooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0E?ooo`030000oooooooo0:_oool001_oool0 0`000?ooooooo`1Doooo00<0003oooooool0Zoooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo0P000?ooool4oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`003Oooo`<00004oooo0P00 00Goool00`000?ooooooo`3ooooo0oooo`003Oooo`040000oooooooo00000_ooo`040000oooooooo 00001?ooo`030000oooooooo0?ooool3oooo000=oooo00@0003oooooool00002oooo00@0003ooooo ool00004oooo0`000?ooool3oooo000=oooo0`0000?oool010000?ooooooo`0000Coool00`000?oo ooooo`3ooooo0oooo`003_ooo`030000oooooooo00;oool010000?ooooooo`0000Coool00`000?oo ooooo`3ooooo0oooo`003_ooo`<00003oooo0P0000Goool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo0P000?ooool4oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0@_ooo`030000oooooooo0;goool001_oool0 0`000?ooooooo`12oooo00<0003oooooool0_Oooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?oo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool000koool200001?ooo`800005oooo00<0003oooooool0ooooo`?oool000goool0 10000?ooooooo`0000;oool010000?ooooooo`0000Coool00`000?ooooooo`0;oooo00<0003ooooo ool06oooo`030000oooooooo0=Koool000goool010000?ooooooo`0000;oool010000?ooooooo`00 00Coool300002oooo`030000oooooooo01_oool00`000?ooooooo`3Foooo000>oooo0P0000?oool0 10000?ooooooo`0000Coool00`000?ooooooo`3ooooo0oooo`003Oooo`040000oooooooo00000_oo o`040000oooooooo00001?ooo`030000oooooooo0?ooool3oooo000>oooo0P0000Coool200001Ooo o`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0>Ooo o`030000oooooooo0_ooo`030000oooooooo07oool000Woool01@000?oo ooooooooo`000002oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`@000001Oooo`00 0?ooooooo`00000Hoooo00<0003oooooool0hOooo`002Oooo`050000oooooooooooo000000;oool0 10000?ooooooo`0000;oool00`000?ooooooo`3ooooo2?ooo`002Oooo`050000oooooooooooo0000 00;oool010000?ooooooo`0000;oool00`000?ooooooo`3ooooo2?ooo`002?ooo`800004oooo0P00 00Coool20000ooooo`_oool00?oooolQoooo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -7.64114, \ 0.607629, 0.624232}}] }, Open ]], Cell[TextData[{ StyleBox["\tWhat happens to the accuracy of the guess as we catch more \ fish? At what point do you think you would 'guarantee' being within 20 \ percent of the actual population? We could make the visualization easier with \ some lines at the appropriate percentages, which we can create as a function \ using ", FontSize->14], StyleBox["Plot.", "Input", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(EstHi20 = \ Plot[\((1 + 20/100)\)*PopSize, {x, 0, PopSize}];\)\), "\[IndentingNewLine]", \(\(EstLo20\ = \ Plot[\((1 - 20/100)\)*PopSize, {x, 0, PopSize}];\)\), "\[IndentingNewLine]", \(\(Err20\ = \ Plot[20, {x, 0, PopSize}];\)\)}], "Input"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 0.0147151 0.00163501 [ [.15079 .00222 -6 -9 ] [.15079 .00222 6 0 ] [.27778 .00222 -6 -9 ] [.27778 .00222 6 0 ] [.40476 .00222 -6 -9 ] [.40476 .00222 6 0 ] [.53175 .00222 -6 -9 ] [.53175 .00222 6 0 ] [.65873 .00222 -9 -9 ] [.65873 .00222 9 0 ] [.78571 .00222 -9 -9 ] [.78571 .00222 9 0 ] [.9127 .00222 -9 -9 ] [.9127 .00222 9 0 ] [.01131 .09647 -12 -4.5 ] [.01131 .09647 0 4.5 ] [.01131 .17822 -18 -4.5 ] [.01131 .17822 0 4.5 ] [.01131 .25997 -18 -4.5 ] [.01131 .25997 0 4.5 ] [.01131 .34172 -18 -4.5 ] [.01131 .34172 0 4.5 ] [.01131 .42347 -18 -4.5 ] [.01131 .42347 0 4.5 ] [.01131 .50522 -18 -4.5 ] [.01131 .50522 0 4.5 ] [.01131 .58697 -18 -4.5 ] [.01131 .58697 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 .01472 m .15079 .02097 L s [(20)] .15079 .00222 0 1 Mshowa .27778 .01472 m .27778 .02097 L s [(40)] .27778 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(60)] .40476 .00222 0 1 Mshowa .53175 .01472 m .53175 .02097 L s [(80)] .53175 .00222 0 1 Mshowa .65873 .01472 m .65873 .02097 L s [(100)] .65873 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(120)] .78571 .00222 0 1 Mshowa .9127 .01472 m .9127 .02097 L s [(140)] .9127 .00222 0 1 Mshowa .125 Mabswid .05556 .01472 m .05556 .01847 L s .0873 .01472 m .0873 .01847 L s .11905 .01472 m .11905 .01847 L s .18254 .01472 m .18254 .01847 L s .21429 .01472 m .21429 .01847 L s .24603 .01472 m .24603 .01847 L s .30952 .01472 m .30952 .01847 L s .34127 .01472 m .34127 .01847 L s .37302 .01472 m .37302 .01847 L s .43651 .01472 m .43651 .01847 L s .46825 .01472 m .46825 .01847 L s .5 .01472 m .5 .01847 L s .56349 .01472 m .56349 .01847 L s .59524 .01472 m .59524 .01847 L s .62698 .01472 m .62698 .01847 L s .69048 .01472 m .69048 .01847 L s .72222 .01472 m .72222 .01847 L s .75397 .01472 m .75397 .01847 L s .81746 .01472 m .81746 .01847 L s .84921 .01472 m .84921 .01847 L s .88095 .01472 m .88095 .01847 L s .94444 .01472 m .94444 .01847 L s .97619 .01472 m .97619 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .09647 m .03006 .09647 L s [(50)] .01131 .09647 1 0 Mshowa .02381 .17822 m .03006 .17822 L s [(100)] .01131 .17822 1 0 Mshowa .02381 .25997 m .03006 .25997 L s [(150)] .01131 .25997 1 0 Mshowa .02381 .34172 m .03006 .34172 L s [(200)] .01131 .34172 1 0 Mshowa .02381 .42347 m .03006 .42347 L s [(250)] .01131 .42347 1 0 Mshowa .02381 .50522 m .03006 .50522 L s [(300)] .01131 .50522 1 0 Mshowa .02381 .58697 m .03006 .58697 L s [(350)] .01131 .58697 1 0 Mshowa .125 Mabswid .02381 .03107 m .02756 .03107 L s .02381 .04742 m .02756 .04742 L s .02381 .06377 m .02756 .06377 L s .02381 .08012 m .02756 .08012 L s .02381 .11282 m .02756 .11282 L s .02381 .12917 m .02756 .12917 L s .02381 .14552 m .02756 .14552 L s .02381 .16187 m .02756 .16187 L s .02381 .19457 m .02756 .19457 L s .02381 .21092 m .02756 .21092 L s .02381 .22727 m .02756 .22727 L s .02381 .24362 m .02756 .24362 L s .02381 .27632 m .02756 .27632 L s .02381 .29267 m .02756 .29267 L s .02381 .30902 m .02756 .30902 L s .02381 .32537 m .02756 .32537 L s .02381 .35807 m .02756 .35807 L s .02381 .37442 m .02756 .37442 L s .02381 .39077 m .02756 .39077 L s .02381 .40712 m .02756 .40712 L s .02381 .43982 m .02756 .43982 L s .02381 .45617 m .02756 .45617 L s .02381 .47252 m .02756 .47252 L s .02381 .48887 m .02756 .48887 L s .02381 .52157 m .02756 .52157 L s .02381 .53792 m .02756 .53792 L s .02381 .55427 m .02756 .55427 L s .02381 .57062 m .02756 .57062 L s .02381 .60332 m .02756 .60332 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .30902 m .06244 .30902 L .10458 .30902 L .14415 .30902 L .18221 .30902 L .22272 .30902 L .26171 .30902 L .30316 .30902 L .34309 .30902 L .3815 .30902 L .42237 .30902 L .46172 .30902 L .49955 .30902 L .53984 .30902 L .57861 .30902 L .61984 .30902 L .65954 .30902 L .69774 .30902 L .73838 .30902 L .77751 .30902 L .81909 .30902 L .85916 .30902 L .89771 .30902 L .93871 .30902 L .97619 .30902 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgooooo`0001<0000001Goool00`000?ooooooo`06 oooo00<0003oooooool01Oooo`030000oooooooo00Koool00`000?ooooooo`05oooo00<0003ooooo ool01_ooo`030000oooooooo00Koool00`000?ooooooo`05oooo00<0003oooooool01_ooo`030000 oooooooo00Koool00`000?ooooooo`05oooo00<0003oooooool01_ooo`030000oooooooo00Koool0 0`000?ooooooo`05oooo00<0003oooooool01_ooo`030000oooooooo00Goool00`000?ooooooo`06 oooo00<0003oooooool01_ooo`030000oooooooo00Goool00`000?ooooooo`06oooo00<0003ooooo ool01_ooo`030000oooooooo00Goool00`000?ooooooo`06oooo00<0003oooooool01_ooo`030000 oooooooo00Goool00`000?ooooooo`06oooo00<0003oooooool01Oooo`030000oooooooo00Koool0 0`000?ooooooo`06oooo00<0003oooooool01Oooo`030000oooooooo00Koool00`000?ooooooo`05 oooo000Eoooo00<0003oooooool07oooo`030000oooooooo023oool00`000?ooooooo`0Poooo00<0 003oooooool07oooo`030000oooooooo023oool00`000?ooooooo`0Ooooo00<0003oooooool08?oo o`030000oooooooo01Koool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo 0?ooool9oooo000Eoooo0P000?ooool:oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool0 0`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo0P000?ooool: oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Ooo o`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool20000oooo o`[oool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000E oooo00<0003oooooool0ooooo`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3o oooo2Oooo`002?ooo`800004oooo0P0000Goool00`000?ooooooo`3ooooo2Oooo`001oooo`040000 oooooooo00000_ooo`040000oooooooo00001?ooo`030000oooooooo0?ooool9oooo000:oooo00@0 003oooooool00002oooo00<0003oooooool00_ooo`<0003ooooo2Oooo`002?ooo`800003oooo00@0 003oooooool00004oooo00<0003oooooool0ooooo`Woool000Soool00`000?ooooooo`02oooo00@0 003oooooool00004oooo00<0003oooooool0ooooo`Woool000Soool300000oooo`800005oooo00<0 003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`80003ooooo2_oo o`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool0 0`000?ooooooo`3ooooo2Oooo`005Oooo`80003ooooo2_ooo`005Oooo`030000oooooooo0?ooool9 oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Ooo o`030000oooooooo0?ooool9oooo000Eoooo0P000?ooool:oooo000Eoooo00<0003oooooool0oooo o`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000E oooo0P000?ooool:oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3o oooo2Oooo`0000?oool0000000000`0000;oool200001?ooo`800005oooo00<0003oooooool0oooo o`Woool000?oool01@000?ooooooooooo`000002oooo00@0003oooooool00002oooo00<0003ooooo ool00_ooo`030000oooooooo0?ooool9oooo0003oooo00D0003oooooooooool000000_ooo`040000 oooooooo00000_ooo`030000oooooooo00;oool30000ooooo`Woool000?oool01@000?oooooooooo o`000002oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`030000oooooooo0?ooool9 oooo0003oooo00D0003oooooooooool000000_ooo`040000oooooooo00000_ooo`030000oooooooo 00;oool00`000?ooooooo`3ooooo2Oooo`000_ooo`800004oooo0P0000Coool200001Oooo`030000 oooooooo0?ooool9oooo000Eoooo0P000?ooool:oooo000Eoooo00<0003oooooool0ooooo`Woool0 01Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0 003oooooool0ooooo`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3ooooo2Ooo o`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool2 0000ooooo`[oool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9 oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool20000ooooo`[oool001Goool00`000?oo ooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo00000oooo`000000000300000_oo o`800004oooo0P0000Goool00`000?ooooooo`3ooooo2Oooo`000oooo`050000oooooooooooo0000 00;oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0003oooooool0ooooo`Woool0 00?oool00`000?ooooooo`04oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`<0003o oooo2Oooo`000oooo`030000oooooooo00;oool200000oooo`040000oooooooo00001?ooo`030000 oooooooo0?ooool9oooo0003oooo00<0003oooooool00_ooo`030000oooooooo00;oool010000?oo ooooo`0000Coool00`000?ooooooo`3ooooo2Oooo`000_ooo`800004oooo0`0000?oool200001Ooo o`030000oooooooo0?ooool9oooo000Eoooo0P000?ooool:oooo000Eoooo00<0003oooooool0oooo o`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000E oooo00<0003oooooool0ooooo`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3o oooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool0 01Gooooo00001@0000Ooool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo 0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Ooo o`005Oooo`80003ooooo2_ooo`005Oooo`030000oooooooo0?ooool9oooo00000oooo`0000000002 00000oooo`800004oooo0P0000Goool00`000?ooooooo`3ooooo2Oooo`0000?oool0003oool01?oo o`040000oooooooo00000_ooo`040000oooooooo00001?ooo`030000oooooooo0?ooool9oooo0002 oooo00<0003oooooool00_ooo`040000oooooooo00000_ooo`040000oooooooo00001?ooo`<0003o oooo2Oooo`000oooo`050000oooooooooooo000000;oool010000?ooooooo`0000;oool00`000?oo ooooo`02oooo00<0003oooooool0ooooo`Woool00005oooo0000oooooooo000000;oool010000?oo ooooo`0000;oool010000?ooooooo`0000Coool00`000?ooooooo`3ooooo2Oooo`000_ooo`800004 oooo0P0000Coool200001Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0oooo o`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000 oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool20000ooooo`[oool0 01Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0 003oooooool0ooooo`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3ooooo2Ooo o`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool0 0`000?ooooooo`3ooooo2Oooo`005Oooo`80003ooooo2_ooo`005Oooo`030000oooooooo0?ooool9 oooo00000oooo`000000000200000oooo`800004oooo0P0000Goool00`000?ooooooo`3ooooo2Ooo o`0000?oool0003oool01?ooo`040000oooooooo00000_ooo`040000oooooooo00001?ooo`030000 oooooooo0?ooool9oooo0002oooo00<0003oooooool01Oooo`040000oooooooo00000_ooo`030000 oooooooo00;oool30000ooooo`Woool000?oool00`000?ooooooo`02oooo0P0000?oool010000?oo ooooo`0000Coool00`000?ooooooo`3ooooo2Oooo`0000Goool0003oooooool000000oooo`030000 oooooooo00;oool010000?ooooooo`0000Coool00`000?ooooooo`3ooooo2Oooo`000_ooo`800004 oooo0`0000?oool200001Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0oooo o`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000 oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool20000ooooo`[oool0 01Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0 003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`80003ooooo2_oo o`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool0 0`000?ooooooo`3ooooo2Oooo`005Oooo`80003ooooo2_ooo`005Oooo`030000oooooooo0?ooool9 oooo000Eoooo00<0003oooooool0ooooo`Woool000;oool200001?ooo`800004oooo0P0000Goool0 0`000?ooooooo`3ooooo2Oooo`0000Goool0003oooooool000000_ooo`040000oooooooo00000_oo o`040000oooooooo00001?ooo`030000oooooooo0?ooool9oooo0003oooo00D0003oooooooooool0 00000_ooo`040000oooooooo00000_ooo`030000oooooooo00;oool30000ooooo`Woool000Coool0 10000?ooooooo`0000;oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0003ooooo ool0ooooo`Woool00005oooo0000oooooooo000000;oool010000?ooooooo`0000;oool010000?oo ooooo`0000Coool00`000?ooooooo`3ooooo2Oooo`000_ooo`800004oooo0P0000Coool200001Ooo o`030000oooooooo0?ooool9oooo000Eoooo0P000?ooool:oooo000Eoooo00<0003oooooool0oooo o`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000E oooo00<0003oooooool0ooooo`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3o oooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool0 01Goool20000ooooo`[oool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo 0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool20000ooooo`[oool001Goool0 0`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo0002oooo0P0000Coool2 00001?ooo`800005oooo00<0003oooooool0ooooo`Woool00005oooo0000oooooooo000000;oool0 10000?ooooooo`0000;oool010000?ooooooo`0000Coool00`000?ooooooo`3ooooo2Oooo`000ooo o`030000oooooooo00Coool010000?ooooooo`0000;oool00`000?ooooooo`02oooo0`000?ooool9 oooo0004oooo00@0003oooooooooool200000oooo`040000oooooooo00001?ooo`030000oooooooo 0?ooool9oooo00001Oooo`000?ooooooo`000003oooo00<0003oooooool00_ooo`040000oooooooo 00001?ooo`030000oooooooo0?ooool9oooo0002oooo0P0000Coool300000oooo`800005oooo00<0 003oooooool0ooooo`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3ooooo2Ooo o`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool0 0`000?ooooooo`3ooooo2Oooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-12.3894, -28.3138, \ 0.578885, 2.24798}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 0.0147151 0.00245252 [ [.15079 .00222 -6 -9 ] [.15079 .00222 6 0 ] [.27778 .00222 -6 -9 ] [.27778 .00222 6 0 ] [.40476 .00222 -6 -9 ] [.40476 .00222 6 0 ] [.53175 .00222 -6 -9 ] [.53175 .00222 6 0 ] [.65873 .00222 -9 -9 ] [.65873 .00222 9 0 ] [.78571 .00222 -9 -9 ] [.78571 .00222 9 0 ] [.9127 .00222 -9 -9 ] [.9127 .00222 9 0 ] [.01131 .13734 -12 -4.5 ] [.01131 .13734 0 4.5 ] [.01131 .25997 -18 -4.5 ] [.01131 .25997 0 4.5 ] [.01131 .38259 -18 -4.5 ] [.01131 .38259 0 4.5 ] [.01131 .50522 -18 -4.5 ] [.01131 .50522 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 .01472 m .15079 .02097 L s [(20)] .15079 .00222 0 1 Mshowa .27778 .01472 m .27778 .02097 L s [(40)] .27778 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(60)] .40476 .00222 0 1 Mshowa .53175 .01472 m .53175 .02097 L s [(80)] .53175 .00222 0 1 Mshowa .65873 .01472 m .65873 .02097 L s [(100)] .65873 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(120)] .78571 .00222 0 1 Mshowa .9127 .01472 m .9127 .02097 L s [(140)] .9127 .00222 0 1 Mshowa .125 Mabswid .05556 .01472 m .05556 .01847 L s .0873 .01472 m .0873 .01847 L s .11905 .01472 m .11905 .01847 L s .18254 .01472 m .18254 .01847 L s .21429 .01472 m .21429 .01847 L s .24603 .01472 m .24603 .01847 L s .30952 .01472 m .30952 .01847 L s .34127 .01472 m .34127 .01847 L s .37302 .01472 m .37302 .01847 L s .43651 .01472 m .43651 .01847 L s .46825 .01472 m .46825 .01847 L s .5 .01472 m .5 .01847 L s .56349 .01472 m .56349 .01847 L s .59524 .01472 m .59524 .01847 L s .62698 .01472 m .62698 .01847 L s .69048 .01472 m .69048 .01847 L s .72222 .01472 m .72222 .01847 L s .75397 .01472 m .75397 .01847 L s .81746 .01472 m .81746 .01847 L s .84921 .01472 m .84921 .01847 L s .88095 .01472 m .88095 .01847 L s .94444 .01472 m .94444 .01847 L s .97619 .01472 m .97619 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .13734 m .03006 .13734 L s [(50)] .01131 .13734 1 0 Mshowa .02381 .25997 m .03006 .25997 L s [(100)] .01131 .25997 1 0 Mshowa .02381 .38259 m .03006 .38259 L s [(150)] .01131 .38259 1 0 Mshowa .02381 .50522 m .03006 .50522 L s [(200)] .01131 .50522 1 0 Mshowa .125 Mabswid .02381 .03924 m .02756 .03924 L s .02381 .06377 m .02756 .06377 L s .02381 .08829 m .02756 .08829 L s .02381 .11282 m .02756 .11282 L s .02381 .16187 m .02756 .16187 L s .02381 .18639 m .02756 .18639 L s .02381 .21092 m .02756 .21092 L s .02381 .23544 m .02756 .23544 L s .02381 .28449 m .02756 .28449 L s .02381 .30902 m .02756 .30902 L s .02381 .33354 m .02756 .33354 L s .02381 .35807 m .02756 .35807 L s .02381 .40712 m .02756 .40712 L s .02381 .43164 m .02756 .43164 L s .02381 .45617 m .02756 .45617 L s .02381 .48069 m .02756 .48069 L s .02381 .52974 m .02756 .52974 L s .02381 .55427 m .02756 .55427 L s .02381 .57879 m .02756 .57879 L s .02381 .60332 m .02756 .60332 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .30902 m .06244 .30902 L .10458 .30902 L .14415 .30902 L .18221 .30902 L .22272 .30902 L .26171 .30902 L .30316 .30902 L .34309 .30902 L .3815 .30902 L .42237 .30902 L .46172 .30902 L .49955 .30902 L .53984 .30902 L .57861 .30902 L .61984 .30902 L .65954 .30902 L .69774 .30902 L .73838 .30902 L .77751 .30902 L .81909 .30902 L .85916 .30902 L .89771 .30902 L .93871 .30902 L .97619 .30902 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgooooo`0001<0000001Goool00`000?ooooooo`06 oooo00<0003oooooool01Oooo`030000oooooooo00Koool00`000?ooooooo`05oooo00<0003ooooo ool01_ooo`030000oooooooo00Koool00`000?ooooooo`05oooo00<0003oooooool01_ooo`030000 oooooooo00Koool00`000?ooooooo`05oooo00<0003oooooool01_ooo`030000oooooooo00Koool0 0`000?ooooooo`05oooo00<0003oooooool01_ooo`030000oooooooo00Goool00`000?ooooooo`06 oooo00<0003oooooool01_ooo`030000oooooooo00Goool00`000?ooooooo`06oooo00<0003ooooo ool01_ooo`030000oooooooo00Goool00`000?ooooooo`06oooo00<0003oooooool01_ooo`030000 oooooooo00Goool00`000?ooooooo`06oooo00<0003oooooool01Oooo`030000oooooooo00Koool0 0`000?ooooooo`06oooo00<0003oooooool01Oooo`030000oooooooo00Koool00`000?ooooooo`05 oooo000Eoooo00<0003oooooool07oooo`030000oooooooo023oool00`000?ooooooo`0Poooo00<0 003oooooool07oooo`030000oooooooo023oool00`000?ooooooo`0Ooooo00<0003oooooool08?oo o`030000oooooooo01Koool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo 0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Ooo o`005Oooo`80003ooooo2_ooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003ooooo ool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9 oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Ooo o`80003ooooo2_ooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0oooo o`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000E oooo00<0003oooooool0ooooo`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3o oooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool0 01Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0 003oooooool0ooooo`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3ooooo2Ooo o`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool0 0`000?ooooooo`3ooooo2Oooo`002?ooo`800004oooo0P0000Goool00`000?ooooooo`3ooooo2Ooo o`001oooo`040000oooooooo00000_ooo`040000oooooooo00001?ooo`030000oooooooo0?ooool9 oooo000:oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`<0003ooooo2Oooo`002?oo o`800003oooo00@0003oooooool00004oooo00<0003oooooool0ooooo`Woool000Soool00`000?oo ooooo`02oooo00@0003oooooool00004oooo00<0003oooooool0ooooo`Woool000Soool300000ooo o`800005oooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Ooo o`030000oooooooo0?ooool9oooo000Eoooo0P000?ooool:oooo000Eoooo00<0003oooooool0oooo o`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000E oooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000 oooooooo0?ooool9oooo000Eoooo0P000?ooool:oooo000Eoooo00<0003oooooool0ooooo`Woool0 01Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0 003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo 0?ooool9oooo000Eoooo0P000?ooool:oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool0 0`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003ooooo ool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`80003ooooo2_ooo`005Ooo o`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?oo ooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo00000oooo`000000000300000_oo o`800004oooo0P0000Goool00`000?ooooooo`3ooooo2Oooo`000oooo`050000oooooooooooo0000 00;oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0003oooooool0ooooo`Woool0 00?oool01@000?ooooooooooo`000002oooo00@0003oooooool00002oooo00<0003oooooool00_oo o`<0003ooooo2Oooo`000oooo`050000oooooooooooo000000;oool010000?ooooooo`0000;oool0 0`000?ooooooo`02oooo00<0003oooooool0ooooo`Woool000?oool01@000?ooooooooooo`000002 oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`030000oooooooo0?ooool9oooo0002 oooo0P0000Coool200001?ooo`800005oooo00<0003oooooool0ooooo`Woool001Goool00`000?oo ooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0oooo o`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000 oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3o oooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eooooo`0000D00007oooo000Eoooo00<0 003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo 0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Ooo o`005Oooo`030000oooooooo0?ooool9oooo000Eoooo0P000?ooool:oooo000Eoooo00<0003ooooo ool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9 oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Ooo o`030000oooooooo0?ooool9oooo000Eoooo0P000?ooool:oooo000Eoooo00<0003oooooool0oooo o`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo0000 0oooo`000000000300000_ooo`800004oooo0P0000Goool00`000?ooooooo`3ooooo2Oooo`000ooo o`050000oooooooooooo000000;oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0 003oooooool0ooooo`Woool000?oool00`000?ooooooo`04oooo00@0003oooooool00002oooo00<0 003oooooool00_ooo`<0003ooooo2Oooo`000oooo`030000oooooooo00;oool200000oooo`040000 oooooooo00001?ooo`030000oooooooo0?ooool9oooo0003oooo00<0003oooooool00_ooo`030000 oooooooo00;oool010000?ooooooo`0000Coool00`000?ooooooo`3ooooo2Oooo`000_ooo`800004 oooo0`0000?oool200001Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0oooo o`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000E oooo0P000?ooool:oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3o oooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool0 01Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo0P00 0?ooool:oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Ooo o`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool0 0`000?ooooooo`3ooooo2Oooo`005Oooo`80003ooooo2_ooo`005Oooo`030000oooooooo0?ooool9 oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Ooo o`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?oo ooooo`3ooooo2Oooo`005Oooo`80003ooooo2_ooo`005Oooo`030000oooooooo0?ooool9oooo000E oooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000 oooooooo0?ooool9oooo00000oooo`000000000200000oooo`800004oooo0P0000Goool00`000?oo ooooo`3ooooo2Oooo`0000?oool0003oool01?ooo`040000oooooooo00000_ooo`040000oooooooo 00001?ooo`030000oooooooo0?ooool9oooo0002oooo00<0003oooooool00_ooo`040000oooooooo 00000_ooo`040000oooooooo00001?ooo`<0003ooooo2Oooo`000oooo`050000oooooooooooo0000 00;oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0003oooooool0ooooo`Woool0 0005oooo0000oooooooo000000;oool010000?ooooooo`0000;oool010000?ooooooo`0000Coool0 0`000?ooooooo`3ooooo2Oooo`000_ooo`800004oooo0P0000Coool200001Oooo`030000oooooooo 0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Ooo o`005Oooo`80003ooooo2_ooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003ooooo ool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9 oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Ooo o`80003ooooo2_ooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0oooo o`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000E oooo00<0003oooooool0ooooo`Woool001Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`80003o oooo2_ooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool0 01Goool00`000?ooooooo`3ooooo2Oooo`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0 003oooooool0ooooo`Woool001Goool20000ooooo`[oool001Goool00`000?ooooooo`3ooooo2Ooo o`005Oooo`030000oooooooo0?ooool9oooo000Eoooo00<0003oooooool0ooooo`Woool001Goool0 0`000?ooooooo`3ooooo2Oooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-12.3894, -18.8759, \ 0.578885, 1.49865}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 0.0147151 0.0147151 [ [.15079 .00222 -6 -9 ] [.15079 .00222 6 0 ] [.27778 .00222 -6 -9 ] [.27778 .00222 6 0 ] [.40476 .00222 -6 -9 ] [.40476 .00222 6 0 ] [.53175 .00222 -6 -9 ] [.53175 .00222 6 0 ] [.65873 .00222 -9 -9 ] [.65873 .00222 9 0 ] [.78571 .00222 -9 -9 ] [.78571 .00222 9 0 ] [.9127 .00222 -9 -9 ] [.9127 .00222 9 0 ] [.01131 .16187 -12 -4.5 ] [.01131 .16187 0 4.5 ] [.01131 .30902 -12 -4.5 ] [.01131 .30902 0 4.5 ] [.01131 .45617 -12 -4.5 ] [.01131 .45617 0 4.5 ] [.01131 .60332 -12 -4.5 ] [.01131 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 .01472 m .15079 .02097 L s [(20)] .15079 .00222 0 1 Mshowa .27778 .01472 m .27778 .02097 L s [(40)] .27778 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(60)] .40476 .00222 0 1 Mshowa .53175 .01472 m .53175 .02097 L s [(80)] .53175 .00222 0 1 Mshowa .65873 .01472 m .65873 .02097 L s [(100)] .65873 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(120)] .78571 .00222 0 1 Mshowa .9127 .01472 m .9127 .02097 L s [(140)] .9127 .00222 0 1 Mshowa .125 Mabswid .05556 .01472 m .05556 .01847 L s .0873 .01472 m .0873 .01847 L s .11905 .01472 m .11905 .01847 L s .18254 .01472 m .18254 .01847 L s .21429 .01472 m .21429 .01847 L s .24603 .01472 m .24603 .01847 L s .30952 .01472 m .30952 .01847 L s .34127 .01472 m .34127 .01847 L s .37302 .01472 m .37302 .01847 L s .43651 .01472 m .43651 .01847 L s .46825 .01472 m .46825 .01847 L s .5 .01472 m .5 .01847 L s .56349 .01472 m .56349 .01847 L s .59524 .01472 m .59524 .01847 L s .62698 .01472 m .62698 .01847 L s .69048 .01472 m .69048 .01847 L s .72222 .01472 m .72222 .01847 L s .75397 .01472 m .75397 .01847 L s .81746 .01472 m .81746 .01847 L s .84921 .01472 m .84921 .01847 L s .88095 .01472 m .88095 .01847 L s .94444 .01472 m .94444 .01847 L s .97619 .01472 m .97619 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .16187 m .03006 .16187 L s [(10)] .01131 .16187 1 0 Mshowa .02381 .30902 m .03006 .30902 L s [(20)] .01131 .30902 1 0 Mshowa .02381 .45617 m .03006 .45617 L s [(30)] .01131 .45617 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(40)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .13244 m .02756 .13244 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .25016 m .02756 .25016 L s .02381 .27959 m .02756 .27959 L s .02381 .33845 m .02756 .33845 L s .02381 .36788 m .02756 .36788 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .4856 m .02756 .4856 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .30902 m .06244 .30902 L .10458 .30902 L .14415 .30902 L .18221 .30902 L .22272 .30902 L .26171 .30902 L .30316 .30902 L .34309 .30902 L .3815 .30902 L .42237 .30902 L .46172 .30902 L .49955 .30902 L .53984 .30902 L .57861 .30902 L .61984 .30902 L .65954 .30902 L .69774 .30902 L .73838 .30902 L .77751 .30902 L .81909 .30902 L .85916 .30902 L .89771 .30902 L .93871 .30902 L .97619 .30902 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-10.71, -3.0988, 0.579268, \ 0.24994}}] }, Open ]] }, Open ]], Cell[TextData[{ StyleBox["\t", FontSize->14], StyleBox["Show", "Input", FontSize->14], StyleBox[" is useful to combine graphics pictures.", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Show[PlotEst, EstHi20, EstLo20];\)\), "\n", \(\(Show[PlotErr, Err20];\)\)}], "Input"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 -2.60209e-017 0.00206011 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .10301 -12 -4.5 ] [.01131 .10301 0 4.5 ] [.01131 .20601 -18 -4.5 ] [.01131 .20601 0 4.5 ] [.01131 .30902 -18 -4.5 ] [.01131 .30902 0 4.5 ] [.01131 .41202 -18 -4.5 ] [.01131 .41202 0 4.5 ] [.01131 .51503 -18 -4.5 ] [.01131 .51503 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .10301 m .03006 .10301 L s [(50)] .01131 .10301 1 0 Mshowa .02381 .20601 m .03006 .20601 L s [(100)] .01131 .20601 1 0 Mshowa .02381 .30902 m .03006 .30902 L s [(150)] .01131 .30902 1 0 Mshowa .02381 .41202 m .03006 .41202 L s [(200)] .01131 .41202 1 0 Mshowa .02381 .51503 m .03006 .51503 L s [(250)] .01131 .51503 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(300)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0206 m .02756 .0206 L s .02381 .0412 m .02756 .0412 L s .02381 .0618 m .02756 .0618 L s .02381 .0824 m .02756 .0824 L s .02381 .12361 m .02756 .12361 L s .02381 .14421 m .02756 .14421 L s .02381 .16481 m .02756 .16481 L s .02381 .18541 m .02756 .18541 L s .02381 .22661 m .02756 .22661 L s .02381 .24721 m .02756 .24721 L s .02381 .26781 m .02756 .26781 L s .02381 .28842 m .02756 .28842 L s .02381 .32962 m .02756 .32962 L s .02381 .35022 m .02756 .35022 L s .02381 .37082 m .02756 .37082 L s .02381 .39142 m .02756 .39142 L s .02381 .43262 m .02756 .43262 L s .02381 .45322 m .02756 .45322 L s .02381 .47383 m .02756 .47383 L s .02381 .49443 m .02756 .49443 L s .02381 .53563 m .02756 .53563 L s .02381 .55623 m .02756 .55623 L s .02381 .57683 m .02756 .57683 L s .02381 .59743 m .02756 .59743 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 .0618 Mdot .03651 0 Mdot .04286 0 Mdot .04921 0 Mdot .05556 0 Mdot .0619 .18541 Mdot .06825 .43262 Mdot .0746 .12361 Mdot .08095 .27812 Mdot .0873 .30902 Mdot .09365 .33992 Mdot .10635 .40172 Mdot .1127 .17305 Mdot .11905 .23176 Mdot .1254 .49443 Mdot .13175 .21013 Mdot .1381 .15892 Mdot .14444 .39142 Mdot .15079 .17658 Mdot .15714 .16223 Mdot .16984 .2843 Mdot .17619 .37082 Mdot .18254 .30902 Mdot .18889 .53563 Mdot .19524 .55623 Mdot .20159 .24721 Mdot .20794 .59743 Mdot .21429 .23176 Mdot .22063 .2737 Mdot .22698 .32962 Mdot .23333 .33992 Mdot .23968 .26266 Mdot .24603 .43262 Mdot .25238 .31785 Mdot .25873 .38112 Mdot .26508 .58713 Mdot .27143 .34433 Mdot .27778 .27468 Mdot .29048 .25957 Mdot .29683 .26575 Mdot .30317 .20918 Mdot .30952 .25283 Mdot .31587 .2843 Mdot .32222 .20748 Mdot .32857 .29666 Mdot .33492 .33649 Mdot .34127 .38627 Mdot .34762 .24246 Mdot .35397 .24721 Mdot .36032 .36395 Mdot .36667 .22249 Mdot .37302 .30902 Mdot .37937 .31464 Mdot .38571 .35228 Mdot .39206 .27574 Mdot .39841 .28049 Mdot .40476 .37082 Mdot .41111 .25133 Mdot .41746 .2737 Mdot .42381 .25957 Mdot .43016 .28253 Mdot .43651 .50215 Mdot .44921 .37644 Mdot .45556 .28018 Mdot .4619 .26653 Mdot .46825 .28842 Mdot .4746 .29254 Mdot .48095 .37082 Mdot .4873 .25065 Mdot .49365 .28584 Mdot .5 .2897 Mdot .50635 .39142 Mdot .5127 .39657 Mdot .51905 .40172 Mdot .5254 .2872 Mdot .53175 .49443 Mdot .5381 .31288 Mdot .54444 .26673 Mdot .55079 .32061 Mdot .55714 .43262 Mdot .56349 .30902 Mdot .56984 .29528 Mdot .57619 .33606 Mdot .58254 .27193 Mdot .58889 .26193 Mdot .59524 .32719 Mdot .60159 .37494 Mdot .60794 .37906 Mdot .61429 .28739 Mdot .62063 .30576 Mdot .62698 .34537 Mdot .63333 .29666 Mdot .63968 .28547 Mdot .64603 .31878 Mdot .65238 .38241 Mdot .65873 .32528 Mdot .66508 .36718 Mdot .67143 .3152 Mdot .67778 .33504 Mdot .68413 .35709 Mdot .69048 .28215 Mdot .69683 .36395 Mdot .70317 .34805 Mdot .70952 .31785 Mdot .71587 .2591 Mdot .72222 .29558 Mdot .72857 .31183 Mdot .73492 .30096 Mdot .74127 .31744 Mdot .74762 .30633 Mdot .75397 .27336 Mdot .76032 .29872 Mdot .76667 .36155 Mdot .77302 .31708 Mdot .77937 .3343 Mdot .78571 .30902 Mdot .79206 .31159 Mdot .79841 .3016 Mdot .80476 .31674 Mdot .81111 .28384 Mdot .81746 .28613 Mdot .82381 .31149 Mdot .83016 .32704 Mdot .83651 .30426 Mdot .84286 .28474 Mdot .84921 .30902 Mdot .85556 .32385 Mdot .8619 .28131 Mdot .86825 .30444 Mdot .8746 .34507 Mdot .88095 .30902 Mdot .8873 .31131 Mdot .89365 .33868 Mdot .9 .31588 Mdot .90635 .29623 Mdot .9127 .29836 Mdot .91905 .31122 Mdot .9254 .31343 Mdot .93175 .33992 Mdot .9381 .29666 Mdot .94444 .32005 Mdot .95079 .31115 Mdot .95714 .30284 Mdot .96349 .31541 Mdot .96984 .30696 Mdot .97619 .30902 Mdot .5 Mabswid .02381 .37082 m .06244 .37082 L .10458 .37082 L .14415 .37082 L .18221 .37082 L .22272 .37082 L .26171 .37082 L .30316 .37082 L .34309 .37082 L .3815 .37082 L .42237 .37082 L .46172 .37082 L .49955 .37082 L .53984 .37082 L .57861 .37082 L .61984 .37082 L .65954 .37082 L .69774 .37082 L .73838 .37082 L .77751 .37082 L .81909 .37082 L .85916 .37082 L .89771 .37082 L .93871 .37082 L .97619 .37082 L s .02381 .24721 m .06244 .24721 L .10458 .24721 L .14415 .24721 L .18221 .24721 L .22272 .24721 L .26171 .24721 L .30316 .24721 L .34309 .24721 L .3815 .24721 L .42237 .24721 L .46172 .24721 L .49955 .24721 L .53984 .24721 L .57861 .24721 L .61984 .24721 L .65954 .24721 L .69774 .24721 L .73838 .24721 L .77751 .24721 L .81909 .24721 L .85916 .24721 L .89771 .24721 L .93871 .24721 L .97619 .24721 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooo00<0003oooooool00_ooo`040000oooooooo00001?ooo`030000oooooooo 0?ooool3oooo000>oooo0`0000?oool200001Oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool02_ooo`030000oooooooo0?Goool001_oool200002oooo`030000oooooooo0?Goool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?oo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool0 0`000?ooooooo`0Joooo00<0003oooooool0iOooo`006oooo`030000oooooooo01[oool00`000?oo ooooo`02oooo00<0003oooooool0h?ooo`006oooo`030000oooooooo01ooool00`000?ooooooo`3P oooo000Koooo0P000?ooool4oooo000Koooo00<0003oooooool05?ooo`030000oooooooo0>_oool0 01_oool00`000?ooooooo`0Doooo00<0003oooooool01oooo`030000oooooooo0>7oool001_oool0 0`000?ooooooo`0Noooo00<0003oooooool0hOooo`006oooo`030000oooooooo00Koool00`000?oo ooooo`3ioooo000Koooo0P0000Ooool00`000?ooooooo`3ioooo000Koooo00<0003oooooool0oooo o`?oool001_oool00`000?ooooooo`3ooooo0oooo`001oooo`D00002oooo0P0000Coool200001Ooo o`030000oooooooo0?ooool3oooo0009oooo00D0003oooooooooool000000_ooo`040000oooooooo 00000_ooo`030000oooooooo00;oool00`000?ooooooo`3ooooo0oooo`002Oooo`050000oooooooo oooo000000;oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo0`0004[oool00`000?oo ooooo`2eoooo0009oooo00D0003oooooooooool000000_ooo`040000oooooooo00000_ooo`030000 oooooooo00;oool00`000?ooooooo`0Ioooo00<0003oooooool0:Oooo`030000oooooooo00;oool0 0`000?ooooooo`2eoooo0009oooo00D0003oooooooooool000000_ooo`040000oooooooo00000_oo o`030000oooooooo00;oool00`000?ooooooo`0Ioooo00<0003oooooool0:Oooo`030000oooooooo 0;[oool000Soool200001?ooo`800004oooo0P0000Goool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo05Goool00`000?ooooooo`2Zoooo000Koooo00<0003oooooool0EOooo`030000 oooooooo0:[oool001_oool200005_ooo`030000oooooooo01Koool00`000?ooooooo`3Aoooo000K oooo00<0003oooooool05Oooo`030000oooooooo01Koool00`000?ooooooo`3Aoooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`1Aoooo00<0003oooooool0[_ooo`006ooo o`030000oooooooo02_oool00`000?ooooooo`0Soooo0P000:ooool001_ooooh00003Oooo`006ooo o`030000oooooooo04Ooool00`000?ooooooo`0Goooo00<0003oooooool04Oooo`030000oooooooo 08[oool001_oool00`000?ooooooo`17oooo00<0003oooooool0I_ooo`030000oooooooo04ooool0 01_oool00`000?ooooooo`0eoooo00<0003oooooool02_ooo`030000oooooooo01ooool00`000?oo ooooo`0Xoooo00<0003oooooool07_ooo`030000oooooooo04ooool001_oool00`000?ooooooo`0e oooo00<0003oooooool02_ooo`80000Poooo00<0003oooooool01oooo`030000oooooooo01?oool0 0`000?ooooooo`08oooo00<0003oooooool0L?ooo`006oooo`800014oooo00<0003oooooool0:?oo o`030000oooooooo01?oool00`000?ooooooo`1koooo000Koooo00<0003oooooool0oooo00<0003oooooool05?ooo`040000oooooooo 00001_ooo`030000oooooooo00Koool00`000?ooooooo`0Ioooo00<0003oool000001_ooo`030000 oooooooo01Goool000Ooool500000_ooo`800004oooo0P0000Goool00`000?ooooooo`2eoooo00<0 003oooooool01?ooo`030000oooooooo00Koool00`000?ooooooo`07oooo00<0003oooooool01Ooo o`030000oooooooo00Woool00`000?ooooooo`09oooo00<0003oooooool04?ooo`002Oooo`050000 oooooooooooo000000;oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0003ooooo ool03Oooo`030000oooooooo01Koool00`000?ooooooo`0^oooo00<0003oooooool0;_ooo`030000 oooooooo00coool00`000?ooooooo`0Noooo00<0003oooooool01oooo`030000oooooooo00[oool0 1@000?ooooooooooo`000003oooo00D0003oooooooooool000004oooo`030000oooooooo0080000> oooo0009oooo00<0003oooooool01?ooo`040000oooooooo00000_ooo`030000oooooooo00;oool3 00003Oooo`030000oooooooo01Koool00`000?ooooooo`0^oooo00<0003oooooool0:?ooo`030000 oooooooo00?oool00`000?ooooooo`0oooo0009oooo00<0 003oooooool00_ooo`800003oooo00@0003oooooool00004oooo00<0003oooooool0FOooo`030000 oooooooo02Koool00`000?ooooooo`0Ooooo00<0003oooooool03?ooo`030000oooooooo00Woool0 0`000?ooooooo`02oooo00@0003oooooool00004oooo00<0003oooooool03Oooo`050000oooooooo oooo000000Coool200001_ooo`040000oooooooo00004Oooo`002Oooo`030000oooooooo00;oool0 0`000?ooooooo`02oooo00@0003oooooool00004oooo00<0003oooooool0>?ooo`030000oooooooo 01koool00`000?ooooooo`0Yoooo00<0003oooooool05_ooo`030000oooooooo00?oool00`000?oo ooooo`07oooo00<0003oooooool01_ooo`030000oooooooo00Goool00`000?ooooooo`05oooo00<0 003oooooool05_ooo`030000oooooooo00?oool00`000?ooooooo`02oooo00<0003oooooool00_oo o`030000oooooooo00ooool000Soool200001?ooo`<00003oooo0P0000Goool00`000?ooooooo`0h oooo00<0003oooooool0B_ooo`030000oooooooo01Koool00`000?ooooooo`0=oooo00<0003ooooo ool01_ooo`030000oooooooo01[oool00`000?ooooooo`0Doooo00<0003oooooool05?ooo`006ooo o`030000oooooooo097oool00`000?ooooooo`0=oooo00<0003oooooool0:_ooo`030000oooooooo 00?oool00`000?ooooooo`0[oooo000Koooo0P0003;oool00`000?ooooooo`1Moooo00<0003ooooo ool03Oooo`030000oooooooo02[oool00`000?ooooooo`0aoooo000Koooo00<0003oooooool0oooo00<0003oooooool01ooo o`030000oooooooo01Ooool001_oool00`000?ooooooo`0moooo00<0003oooooool0FOooo`030000 oooooooo03goool00`000?ooooooo`0Voooo000Koooo00<0003oooooool0?Oooo`030000oooooooo 05Woool00`000?ooooooo`0Aoooo00<0003oooooool0:Oooo`030000oooooooo02Koool001_oool2 0000Foooo`030000oooooooo053oool00`000?ooooooo`1Boooo000Koooo00<0003oooooool0F_oo o`030000oooooooo04_oool00`000?ooooooo`1Goooo000Koooo00<0003oooooool0Z?ooo`030000 oooooooo01;oool00`000?ooooooo`12oooo000Koooo00<0003oooooool0E?ooo`030000oooooooo 04coool00`000?ooooooo`05oooo00<0003oooooool03oooo`030000oooooooo04;oool001_oool0 0`000?ooooooo`0Toooo00<0003oooooool0;Oooo`030000oooooooo00Soool00`000?ooooooo`0A oooo00<0003oooooool0;Oooo`030000oooooooo00Goool00`000?ooooooo`1Doooo000Koooon000 00goool001_oool00`000?ooooooo`1[oooo00<0003oooooool09?ooo`030000oooooooo06goool0 01_oool00`000?ooooooo`0ioooo00<0003oooooool0;oooo`030000oooooooo02Koool00`000?oo ooooo`09oooo00<0003oooooool0Goooo`006oooo`030000oooooooo03Woool00`000?ooooooo`0C oooo00<0003oooooool0@_ooo`030000oooooooo00Woool00`000?ooooooo`1Ooooo000Koooo00<0 003oooooool0Coooo`030000oooooooo0;3oool001_oool200007Oooo`030000oooooooo05_oool0 0`000?ooooooo`25oooo000Koooo00<0003oooooool07?ooo`030000oooooooo05_oool20000Q_oo o`006oooo`030000oooooooo01;oool00`000?ooooooo`1Voooo00<0003oool00000Q?ooo`006ooo o`030000oooooooo01;oool00`000?ooooooo`1Xoooo00<0003oooooool0P_ooo`001oooo`@00003 oooo0P0000Coool200001Oooo`030000oooooooo0?ooool3oooo0007oooo00<0003oooooool00ooo o`040000oooooooo00000_ooo`040000oooooooo00001?ooo`030000oooooooo0?ooool3oooo0008 oooo00<0003oooooool00_ooo`040000oooooooo00000_ooo`040000oooooooo00001?ooo`<0003o oooo0oooo`002Oooo`050000oooooooooooo000000;oool010000?ooooooo`0000;oool00`000?oo ooooo`02oooo00<0003oooooool0ooooo`?oool000Ooool010000?ooooooo`0000;oool010000?oo ooooo`0000;oool010000?ooooooo`0000Coool00`000?ooooooo`3ooooo0oooo`002?ooo`800004 oooo0P0000Coool200001Oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool02?oo o`030000oooooooo02_oool00`000?ooooooo`1>oooo00<0003oooooool0N?ooo`006oooo`800009 oooo00<0003oooooool0:oooo`030000oooooooo04koool00`000?ooooooo`1hoooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo0P000?ooool4oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool05ooo o`030000oooooooo06Koool00`000?ooooooo`1ooooo000Koooo0P0001Soool00`000?ooooooo`1V oooo00<0003oooooool0Ooooo`006oooo`030000oooooooo06Soool00`000?ooooooo`2Goooo000K oooo00<0003oooooool0J?ooo`030000oooooooo09Ooool000Ooool400000oooo`800004oooo0P00 00Goool00`000?ooooooo`3ooooo0oooo`001oooo`030000oooooooo00?oool010000?ooooooo`00 00;oool010000?ooooooo`0000Coool00`000?ooooooo`3ooooo0oooo`002?ooo`030000oooooooo 00Goool010000?ooooooo`0000;oool00`000?ooooooo`02oooo0`000?ooool3oooo0009oooo00<0 003oooooool00_ooo`800003oooo00@0003oooooool00004oooo00<0003oooooool0ooooo`?oool0 00Ooool010000?ooooooo`0000?oool00`000?ooooooo`02oooo00@0003oooooool00004oooo00<0 003oooooool0ooooo`?oool000Soool200001?ooo`<00003oooo0P0000Goool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool09oooo`030000 oooooooo0=Soool001_oool20000:?ooo`030000oooooooo0=Soool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`0Yoooo00<0003oooooool0e_ooo`006oooo`80000Zoooo00<0003ooooo ool0e_ooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo0P00 0?ooool4oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`0koooo00<0 003oooooool0a?ooo`006oooo`030000oooooooo03_oool00`000?ooooooo`34oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`0/oooo00<0003oooooool0doooo`006ooo o`80000]oooo00<0003oooooool0doooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool000Soool200001?ooo`800004oooo0P0000Goool00`000?ooooooo`3o oooo0oooo`001oooo`040000oooooooo00000_ooo`040000oooooooo00000_ooo`040000oooooooo 00001?ooo`030000oooooooo0?ooool3oooo0009oooo00D0003oooooooooool000000_ooo`040000 oooooooo00000_ooo`030000oooooooo00;oool30000ooooo`?oool000[oool010000?ooooooo`00 00;oool010000?ooooooo`0000;oool00`000?ooooooo`3ooooo2?ooo`001oooo`040000oooooooo 00000_ooo`040000oooooooo00000_ooo`040000oooooooo0000ooooo`[oool000Soool200001?oo o`800004oooo0P000?ooool;oooo003ooooo8Oooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -22.9235, \ 0.607629, 1.8727}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 1.73472e-017 0.00618034 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .12361 -12 -4.5 ] [.01131 .12361 0 4.5 ] [.01131 .24721 -12 -4.5 ] [.01131 .24721 0 4.5 ] [.01131 .37082 -12 -4.5 ] [.01131 .37082 0 4.5 ] [.01131 .49443 -12 -4.5 ] [.01131 .49443 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .12361 m .03006 .12361 L s [(20)] .01131 .12361 1 0 Mshowa .02381 .24721 m .03006 .24721 L s [(40)] .01131 .24721 1 0 Mshowa .02381 .37082 m .03006 .37082 L s [(60)] .01131 .37082 1 0 Mshowa .02381 .49443 m .03006 .49443 L s [(80)] .01131 .49443 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(100)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0309 m .02756 .0309 L s .02381 .0618 m .02756 .0618 L s .02381 .09271 m .02756 .09271 L s .02381 .15451 m .02756 .15451 L s .02381 .18541 m .02756 .18541 L s .02381 .21631 m .02756 .21631 L s .02381 .27812 m .02756 .27812 L s .02381 .30902 m .02756 .30902 L s .02381 .33992 m .02756 .33992 L s .02381 .40172 m .02756 .40172 L s .02381 .43262 m .02756 .43262 L s .02381 .46353 m .02756 .46353 L s .02381 .52533 m .02756 .52533 L s .02381 .55623 m .02756 .55623 L s .02381 .58713 m .02756 .58713 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 .61803 Mdot .03651 .61803 Mdot .04286 .61803 Mdot .04921 .12361 Mdot .05556 .61803 Mdot .0619 .12361 Mdot .06825 .24721 Mdot .0746 .12361 Mdot .08095 .49443 Mdot .0873 .30902 Mdot .1 .12361 Mdot .10635 .18541 Mdot .1127 .24721 Mdot .11905 .15451 Mdot .13175 .09271 Mdot .1381 .17305 Mdot .14444 .14833 Mdot .15079 .61803 Mdot .16349 .07416 Mdot .17619 .02472 Mdot .18254 .10301 Mdot .18889 .18541 Mdot .19524 .49443 Mdot .20159 .07416 Mdot .20794 .27812 Mdot .21429 .08829 Mdot .22063 .07063 Mdot .22698 .05297 Mdot .23333 .03532 Mdot .23968 .19777 Mdot .24603 .10301 Mdot .25238 .24721 Mdot .25873 .52533 Mdot .26508 .0309 Mdot .27143 .0824 Mdot .27778 .06867 Mdot .28413 .11125 Mdot .29048 .42026 Mdot .29683 .08652 Mdot .30317 .07416 Mdot .30952 0 Mdot .31587 .19424 Mdot .32222 .03708 Mdot .32857 .56859 Mdot .33492 .24721 Mdot .34127 .06867 Mdot .34762 .04495 Mdot .35397 .09614 Mdot .36032 .31785 Mdot .36667 .0618 Mdot .37302 .13734 Mdot .37937 .0412 Mdot .38571 .14833 Mdot .39206 .0206 Mdot .39841 .11125 Mdot .40476 .20601 Mdot .41111 .06742 Mdot .41746 .0206 Mdot .42381 .18541 Mdot .43016 .09064 Mdot .43651 0 Mdot .44286 .0618 Mdot .44921 .21013 Mdot .45556 .22249 Mdot .4619 .15732 Mdot .46825 .07725 Mdot .4746 .05705 Mdot .48095 .0618 Mdot .4873 .20227 Mdot .49365 .00824 Mdot .5 0 Mdot .50635 .10459 Mdot .5127 .08927 Mdot .51905 .1106 Mdot .5254 .07946 Mdot .53175 .08829 Mdot .5381 .0618 Mdot .54444 .13538 Mdot .55079 .04807 Mdot .55714 .00727 Mdot .56349 .0824 Mdot .56984 .11183 Mdot .57619 .10595 Mdot .58254 .07416 Mdot .58889 .00687 Mdot .59524 .03635 Mdot .60159 .05562 Mdot .60794 .14009 Mdot .61429 .05817 Mdot .62063 .00651 Mdot .62698 .07271 Mdot .63333 .05297 Mdot .63968 .04709 Mdot .64603 .09452 Mdot .65238 .02602 Mdot .65873 .02943 Mdot .66508 .05057 Mdot .67143 .04554 Mdot .67778 .03933 Mdot .68413 .05855 Mdot .69048 .0309 Mdot .69683 .04837 Mdot .70317 .06695 Mdot .70952 .01124 Mdot .71587 .05665 Mdot .72222 .13734 Mdot .72857 .0215 Mdot .73492 .0412 Mdot .74127 .01075 Mdot .74762 .02247 Mdot .75397 0 Mdot .76032 .09889 Mdot .76667 .03933 Mdot .77302 .04495 Mdot .77937 .02967 Mdot .78571 .02687 Mdot .79206 .01978 Mdot .79841 .01483 Mdot .80476 .07304 Mdot .81111 .11183 Mdot .81746 .05374 Mdot .82381 .00494 Mdot .83016 .01426 Mdot .83651 .0412 Mdot .84286 .00475 Mdot .84921 .04415 Mdot .85556 .05665 Mdot .8619 .09136 Mdot .86825 .06695 Mdot .8746 .00458 Mdot .88095 .07725 Mdot .8873 .01766 Mdot .89365 .0341 Mdot .9 .02984 Mdot .90635 .00441 Mdot .9127 .02289 Mdot .91905 .01705 Mdot .9254 .01279 Mdot .93175 .02884 Mdot .9381 .02472 Mdot .94444 0 Mdot .95079 .01648 Mdot .95714 .01236 Mdot .96349 .00824 Mdot .96984 .00412 Mdot .97619 0 Mdot .5 Mabswid .02381 .12361 m .06244 .12361 L .10458 .12361 L .14415 .12361 L .18221 .12361 L .22272 .12361 L .26171 .12361 L .30316 .12361 L .34309 .12361 L .3815 .12361 L .42237 .12361 L .46172 .12361 L .49955 .12361 L .53984 .12361 L .57861 .12361 L .61984 .12361 L .65954 .12361 L .69774 .12361 L .73838 .12361 L .77751 .12361 L .81909 .12361 L .85916 .12361 L .89771 .12361 L .93871 .12361 L .97619 .12361 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooo00<0003oooooool01oooo`030000oooooooo 00goool01@000?ooooooooooo`00000^oooo000Koooo00<0003oooooool0DOooo`030000oooooooo 037oool00`000?ooooooo`0Doooo00<0003oooooool01?ooo`800006oooo00<0003oooooool04Ooo o`030000oooooooo017oool00`000?ooooooo`0/oooo000Koooo00<0003oooooool0oooo00<0003oooooool03Oooo`050000oooooooooooo0000017oool00`000?ooooooo`05 oooo00<0003oooooool08Oooo`030000oooooooo02_oool001_oool20000E_ooo`030000oooooooo 017oool00`000?ooooooo`07oooo00<0003oooooool03?ooo`030000oooooooo07goool001_oool0 0`000?ooooooo`0noooo00<0003oooooool03_ooo`030000oooooooo00ooool00`000?ooooooo`19 oooo00<0003oooooool09oooo`030000oooooooo02Soool001_oool00`000?ooooooo`0`oooo00<0 003oooooool02oooo`030000oooooooo00koool00`000?ooooooo`0?oooo00<0003oooooool0=Ooo o`030000oooooooo017oool00`000?ooooooo`0Goooo00<0003oooooool03Oooo`030000oooooooo 02Soool001_oool00`000?ooooooo`0Qoooo00<0003oooooool01oooo`030000oooooooo00;oool0 0`000?ooooooo`0Boooo00<0003oooooool0:?ooo`030000oooooooo01[oool00`000?ooooooo`09 oooo00<0003oooooool0:oooo`030000oooooooo017oool00`000?ooooooo`0Toooo000Koooo00<0 003oooooool08Oooo`030000oooooooo00Ooool00`000?ooooooo`0Goooo00<0003oooooool0:?oo o`030000oooooooo00coool00`000?ooooooo`0;oooo00<0003oooooool0Boooo`030000oooooooo 02Coool001_oool00`000?ooooooo`0moooo00<0003oooooool0?oooo`030000oooooooo00Koool0 0`000?ooooooo`1goooo000Koooo00<0003oooooool0;_ooo`030000oooooooo00coool00`000?oo ooooo`03oooo00<0003oooooool0=Oooo`030000oooooooo00;oool00`000?ooooooo`05oooo00<0 003oooooool0Moooo`006oooo`030000oooooooo01Woool00`000?ooooooo`0Boooo00<0003ooooo ool04_ooo`030000oooooooo023oool00`000?ooooooo`0Boooo00<0003oooooool00_ooo`030000 oooooooo05?oool00`000?ooooooo`0Yoooo000Koooo0P0001[oool00`000?ooooooo`0foooo00<0 003oooooool04Oooo`030000oooooooo03Goool00`000?ooooooo`0eoooo00<0003oooooool0:Ooo o`006oooo`030000oooooooo05;oool00`000?ooooooo`19oooo00<0003oooooool06oooo`030000 oooooooo04?oool001_oool00`000?ooooooo`0Voooo00<0003oooooool03Oooo`030000oooooooo 047oool00`000?ooooooo`0ooooo00<0003oooooool0@oooo`006oooo`030000oooooooo02Koool0 0`000?ooooooo`0=oooo00<0003oooooool0@Oooo`030000oooooooo00ooool00`000?ooooooo`1c oooo000Koooo00<0003oooooool0@?ooo`030000oooooooo01_oool00`000?ooooooo`0Loooo00<0 003oooooool02_ooo`030000oooo000003coool00`000?ooooooo`0foooo000Koooo00<0003ooooo ool0@?ooo`030000oooooooo01_oool00`000?ooooooo`0Loooo00<0003oooooool02_ooo`030000 oooooooo03coool00`000?ooooooo`0foooo000=oooo100000?oool200001Oooo`030000oooooooo 0?ooool3oooo000=oooo00<0003oooooool00oooo`040000oooooooo00001?ooo`030000oooooooo 00?oool010000?ooooooo`0000?oool00`000?ooooooo`03oooo00<0003oooooool0koooo`003_oo o`030000oooooooo00;oool010000?ooooooo`0000Cooooh00003Oooo`003oooo`050000oooooooo oooo000000;oool00`000?ooooooo`02oooo00<0003oooooool0ooooo`?oool000goool010000?oo ooooo`0000;oool010000?ooooooo`0000Coool00`000?ooooooo`24oooo00<0003oooooool0Nooo o`003_ooo`800004oooo0P0000Goool00`000?ooooooo`1Goooo00<0003oooooool0:_ooo`030000 oooooooo02_oool00`000?ooooooo`1=oooo000Koooo00<0003oooooool0Eoooo`030000oooooooo 03[oool00`000?ooooooo`0Koooo00<0003oooooool0COooo`006oooo`030000oooooooo09Coool0 0`000?ooooooo`1[oooo000Koooo00<0003oooooool07?ooo`030000oooooooo03_oool00`000?oo ooooo`2Uoooo000Koooo00<0003oooooool05Oooo`030000oooooooo00Coool00`000?ooooooo`0k oooo00<0003oooooool0YOooo`006oooo`80000Foooo00<0003oooooool0E_ooo`030000oooooooo 097oool001_oool00`000?ooooooo`1^oooo00<0003oooooool0TOooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`0Joooo00<0 003oooooool0iOooo`006oooo`030000oooooooo01[oool00`000?ooooooo`3Uoooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`0Boooo00<0003oooooool04_ooo`030000 oooooooo03[oool00`000?ooooooo`2Koooo000Koooo0P0001?oool00`000?ooooooo`0Boooo00<0 003oooooool0>_ooo`030000oooooooo09_oool001_oool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo04Soool00`000?ooooooo`2goooo000Koooo00<0003oooooool0=Oooo`030000 oooooooo013oool00`000?ooooooo`2goooo000Koooo00<0003oooooool0=Oooo`030000oooooooo 03goool00`000?ooooooo`2:oooo000Koooo00<0003oooooool0Goooo`030000oooooooo01?oool0 0`000?ooooooo`2:oooo000Koooo00<0003oooooool0Goooo`030000oooooooo00Woool00`000?oo ooooo`2Doooo000Koooo00<0003oooooool0Joooo`030000oooooooo09Coool001_oool20000oooo o`Coool001_oool00`000?ooooooo`1]oooo00<0003oooooool0T_ooo`006oooo`030000oooooooo 06goool00`000?ooooooo`2Boooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000?oooo0`0000;oool200001Ooo o`030000oooooooo0?ooool3oooo000@oooo00@0003oooooool00002oooo00<0003oooooool00_oo o`030000oooooooo00Soool00`000?ooooooo`09oooo00<0003oooooool08Oooo`030000oooooooo 01;oool00`000?ooooooo`2boooo000=oooo1@000005oooo0000oooooooo000000Coool300002?oo o`030000oooooooo00Woool00`000?ooooooo`0Qoooo00<0003oooooool04_ooo`030000oooooooo 0;;oool000goool010000?ooooooo`0000;oool010000?ooooooo`0000Coool00`000?ooooooo`3o oooo0oooo`003_ooo`030000oooo000000;oool010000?ooooooo`0000Coool00`000?ooooooo`3o oooo0oooo`003oooo`800003oooo0P0000Goool00`000?ooooooo`3ooooo0oooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo02coool00`000?ooooooo`3Coooo000Koooo0P0002goool0 0`000?ooooooo`3Coooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool03Oooo`030000oooooooo0?;oool001_oool200003_ooo`030000oooooooo0?;oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo05Coool00`000?ooooooo`2[ oooo000Koooo00<0003oooooool0E?ooo`030000oooooooo0:_oool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?ooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool000goool3 00001?ooo`800005oooo00<0003oooooool0ooooo`?oool000goool010000?ooooooo`0000;oool0 10000?ooooooo`0000Coool00`000?ooooooo`3ooooo0oooo`003Oooo`040000oooooooo00000_oo o`040000oooooooo00001?ooo`<0003ooooo0oooo`003Oooo`<00003oooo00@0003oooooool00004 oooo00<0003oooooool0ooooo`?oool000koool00`000?ooooooo`02oooo00@0003oooooool00004 oooo00<0003oooooool0ooooo`?oool000koool300000oooo`800005oooo00<0003oooooool0oooo o`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003o oooo1?ooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo04;oool00`000?ooooooo`2m oooo000Koooo00<0003oooooool0@_ooo`030000oooooooo0;goool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo0P000?ooool4oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool2 0000ooooo`Coool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo0?ooool3oooo000>oooo0P0000Coool200001Oooo`030000oooooooo0?ooool3 oooo000=oooo00@0003oooooool00002oooo00@0003oooooool00004oooo00<0003oooooool02ooo o`030000oooooooo01_oool00`000?ooooooo`3Foooo000=oooo00@0003oooooool00002oooo00@0 003oooooool00004oooo0`0000_oool00`000?ooooooo`0Koooo00<0003oooooool0e_ooo`003_oo o`800003oooo00@0003oooooool00004oooo00<0003oooooool0ooooo`?oool000goool010000?oo ooooo`0000;oool010000?ooooooo`0000Coool00`000?ooooooo`3ooooo0oooo`003_ooo`800004 oooo0P0000Goool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000 oooooooo03Woool00`000?ooooooo`36oooo000Koooo0P0003[oool00`000?ooooooo`36oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool20000ooooo`Coool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0C?ooo`030000oooooooo0;?oool001_oool00`000?oo ooooo`17oool000Woool01@000?oooooooooo o`000002oooo00@0003oooooool00002oooo00<0003oooooool0ooooo`Soool000Woool01@000?oo ooooooooo`000002oooo00@0003oooooool00002oooo00<0003oooooool0ooooo`Soool000Soool2 00001?ooo`800004oooo0P000?ooool;oooo003ooooo8Oooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -7.64114, \ 0.607629, 0.624232}}] }, Open ]] }, Open ]], Cell[TextData[{ StyleBox["\tLet us try the same study, but this time we will vary the \ number of fish we tag, and keep constant (at 30) the number in the second \ catch (switching ", FontSize->14], StyleBox["i", "Input", FontSize->14], StyleBox[" and 30 in ", FontSize->14], StyleBox["GuessPop", "Input", FontSize->14], StyleBox[").", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(PopSize\ = \ 150;\)\), "\[IndentingNewLine]", \(\(Est1Catch\ = \[IndentingNewLine]Table[\(GuessPop[PopSize, i, 30]\)[\([1]\)], {i, PopSize}];\)\), "\[IndentingNewLine]", \(\(Err1Catch\ = \[IndentingNewLine]Table[\(GuessPop[PopSize, i, 30]\)[\([3]\)], {i, PopSize}];\)\), "\[IndentingNewLine]", \(\(PlotEst\ = \ ListPlot[Est1Catch, PlotRange \[Rule] {0, 2*PopSize}];\)\), "\[IndentingNewLine]", \(\(PlotErr\ = \ ListPlot[Err1Catch, PlotRange \[Rule] {0, 100}];\)\), "\[IndentingNewLine]", \(\(Show[PlotEst, EstHi20, EstLo20];\)\), "\n", \(\(Show[PlotErr, Err20];\)\)}], "Input"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 -2.60209e-017 0.00206011 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .10301 -12 -4.5 ] [.01131 .10301 0 4.5 ] [.01131 .20601 -18 -4.5 ] [.01131 .20601 0 4.5 ] [.01131 .30902 -18 -4.5 ] [.01131 .30902 0 4.5 ] [.01131 .41202 -18 -4.5 ] [.01131 .41202 0 4.5 ] [.01131 .51503 -18 -4.5 ] [.01131 .51503 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .10301 m .03006 .10301 L s [(50)] .01131 .10301 1 0 Mshowa .02381 .20601 m .03006 .20601 L s [(100)] .01131 .20601 1 0 Mshowa .02381 .30902 m .03006 .30902 L s [(150)] .01131 .30902 1 0 Mshowa .02381 .41202 m .03006 .41202 L s [(200)] .01131 .41202 1 0 Mshowa .02381 .51503 m .03006 .51503 L s [(250)] .01131 .51503 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(300)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0206 m .02756 .0206 L s .02381 .0412 m .02756 .0412 L s .02381 .0618 m .02756 .0618 L s .02381 .0824 m .02756 .0824 L s .02381 .12361 m .02756 .12361 L s .02381 .14421 m .02756 .14421 L s .02381 .16481 m .02756 .16481 L s .02381 .18541 m .02756 .18541 L s .02381 .22661 m .02756 .22661 L s .02381 .24721 m .02756 .24721 L s .02381 .26781 m .02756 .26781 L s .02381 .28842 m .02756 .28842 L s .02381 .32962 m .02756 .32962 L s .02381 .35022 m .02756 .35022 L s .02381 .37082 m .02756 .37082 L s .02381 .39142 m .02756 .39142 L s .02381 .43262 m .02756 .43262 L s .02381 .45322 m .02756 .45322 L s .02381 .47383 m .02756 .47383 L s .02381 .49443 m .02756 .49443 L s .02381 .53563 m .02756 .53563 L s .02381 .55623 m .02756 .55623 L s .02381 .57683 m .02756 .57683 L s .02381 .59743 m .02756 .59743 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 0 Mdot .03651 .12361 Mdot .04286 0 Mdot .04921 .24721 Mdot .05556 .15451 Mdot .0619 .37082 Mdot .06825 0 Mdot .0746 .16481 Mdot .08095 .27812 Mdot .0873 .20601 Mdot .09365 .13597 Mdot .1 .24721 Mdot .10635 .26781 Mdot .1127 .21631 Mdot .1254 .32962 Mdot .13175 .26266 Mdot .1381 .27812 Mdot .14444 .29357 Mdot .15079 .61803 Mdot .15714 .32447 Mdot .16349 .22661 Mdot .18254 .30902 Mdot .18889 .32138 Mdot .19524 .20859 Mdot .20159 .3461 Mdot .20794 .35846 Mdot .21429 .37082 Mdot .22063 .38318 Mdot .22698 .21975 Mdot .23333 .33992 Mdot .23968 .35022 Mdot .24603 .21631 Mdot .25238 .31785 Mdot .25873 .38112 Mdot .26508 .29357 Mdot .27143 .40172 Mdot .27778 .27468 Mdot .28413 .42232 Mdot .29048 .37082 Mdot .29683 .29528 Mdot .30317 .33992 Mdot .30952 .55623 Mdot .31587 .25845 Mdot .32222 .26407 Mdot .32857 .29666 Mdot .33492 .43262 Mdot .34127 .28092 Mdot .34762 .35022 Mdot .35397 .32138 Mdot .36032 .29778 Mdot .36667 .41717 Mdot .37302 .26148 Mdot .37937 .3461 Mdot .38571 .35228 Mdot .39206 .32587 Mdot .39841 .24309 Mdot .40476 .28525 Mdot .41111 .34273 Mdot .41746 .34835 Mdot .42381 .35396 Mdot .43016 .49443 Mdot .43651 .40172 Mdot .44286 .29136 Mdot .44921 .37644 Mdot .45556 .35022 Mdot .4619 .25085 Mdot .46825 .39329 Mdot .4746 .29254 Mdot .48095 .24721 Mdot .4873 .26539 Mdot .49365 .38112 Mdot .5 .24396 Mdot .50635 .24721 Mdot .5127 .33992 Mdot .51905 .26781 Mdot .5254 .2872 Mdot .53175 .29084 Mdot .5381 .26348 Mdot .54444 .31674 Mdot .55079 .25648 Mdot .55714 .27324 Mdot .56349 .35022 Mdot .56984 .27974 Mdot .57619 .29872 Mdot .58254 .28625 Mdot .58889 .32356 Mdot .59524 .34764 Mdot .60159 .40172 Mdot .60794 .24721 Mdot .61429 .35923 Mdot .62063 .32275 Mdot .62698 .32618 Mdot .63333 .31227 Mdot .63968 .28547 Mdot .64603 .31878 Mdot .65238 .30593 Mdot .65873 .28092 Mdot .66508 .32853 Mdot .67143 .30019 Mdot .67778 .35365 Mdot .68413 .33829 Mdot .69048 .30902 Mdot .69683 .28483 Mdot .70317 .26452 Mdot .70952 .29021 Mdot .71587 .35456 Mdot .72222 .30902 Mdot .72857 .26385 Mdot .73492 .3461 Mdot .74127 .27935 Mdot .74762 .29357 Mdot .75397 .29614 Mdot .76032 .29872 Mdot .76667 .28924 Mdot .77302 .31708 Mdot .77937 .29418 Mdot .78571 .30902 Mdot .79206 .28762 Mdot .79841 .3016 Mdot .80476 .29238 Mdot .81111 .3332 Mdot .81746 .32189 Mdot .82381 .26853 Mdot .83016 .2907 Mdot .83651 .34395 Mdot .84286 .31891 Mdot .84921 .29757 Mdot .85556 .32385 Mdot .8619 .28131 Mdot .86825 .29357 Mdot .8746 .28557 Mdot .88095 .30902 Mdot .8873 .30019 Mdot .89365 .3136 Mdot .9 .3046 Mdot .90635 .31817 Mdot .9127 .29836 Mdot .91905 .30049 Mdot .9254 .30262 Mdot .93175 .32733 Mdot .9381 .30689 Mdot .94444 .30902 Mdot .95079 .30078 Mdot .95714 .30284 Mdot .96349 .3049 Mdot .96984 .30696 Mdot .97619 .30902 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooo0P0000Coool200001Oooo`030000oooooooo0?ooool3oooo000=oooo00@0003ooooo ool00002oooo00@0003oooooool00004oooo00<0003oooooool0ooooo`?oool0013oool010000?oo ooooo`0000;oool00`000?ooooooo`02oooo0`000?ooool3oooo000>oooo0P0000?oool010000?oo ooooo`0000Coool00`000?ooooooo`3ooooo0oooo`003_ooo`030000oooooooo00;oool010000?oo ooooo`0000Coool00`000?ooooooo`3ooooo0oooo`003_ooo`<00003oooo0P0000Goool00`000?oo ooooo`3ooooo0oooo`006oooo`040000oooooooo0000ooooo`;oool001_oool2000000?oool0003o ool0ooooo`7oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool03oooo`030000oooooooo0?3oool001_oool00`000?ooooooo`0? oooo00<0003oooooool0l?ooo`006oooo`80003ooooo1?ooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool01Oooo`030000oooooooo0?[oool001_oool00`000?ooooooo`05 oooo00<0003oooooool0n_ooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool02_ooo`030000oooooooo0?Goool001_oool200002oooo`030000oooooooo0?Goool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?ooo`006ooo o`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool000Ooool500000_oo o`800004oooo0P0000Goool00`000?ooooooo`3ooooo0oooo`002Oooo`050000oooooooooooo0000 00;oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0003oooooool0ooooo`?oool0 00Woool01@000?ooooooooooo`000002oooo00@0003oooooool00002oooo00<0003oooooool00_oo o`<0000=oooo00<0003oooooool06Oooo`030000oooooooo0=Koool000Woool01@000?oooooooooo o`000002oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`030000oooooooo00goool0 0`000?ooooooo`0Ioooo00<0003oooooool0e_ooo`002Oooo`050000oooooooooooo000000;oool0 10000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0003oooooool05?ooo`030000oooooooo 01ooool00`000?ooooooo`39oooo0008oooo0P0000Coool200001?ooo`800005oooo00<0003ooooo ool05?ooo`030000oooooooo01[oool00`000?ooooooo`02oooo00<0003oooooool0bOooo`006ooo o`030000oooooooo037oool00`000?ooooooo`3>oooo000Koooo00<0003oooooool08Oooo`030000 oooooooo0=koool001_oool200008_ooo`030000oooooooo0=koool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0G_ooo`030000 oooooooo0:7oool001_oool00`000?ooooooo`03oooo00<0003oooooool02_ooo`030000oooooooo 04_oool00`000?ooooooo`0Boooo00<0003oooooool00_ooo`030000oooo000001Woool00`000?oo ooooo`1[oooo000Koooo0P0000Coool00`000?ooooooo`0:oooo00<0003oooooool0Foooo`030000 oooooooo00;oool00`000?ooooooo`02oooo00<0003oool000006Oooo`030000oooooooo06_oool0 01_oool00`000?ooooooo`1^oooo00<0003oooooool0TOooo`006oooo`030000oooooooo04Soool0 0`000?ooooooo`0joooo00<0003oooooool0N_ooo`006oooo`030000oooooooo01Woool00`000?oo ooooo`0/oooo00<0003oooooool03?ooo`030000oooooooo02_oool00`000?ooooooo`1joooo000K oooo00<0003oooooool06Oooo`030000oooooooo02koool00`000?ooooooo`0:oooo00<0003ooooo ool06oooo`030000oooooooo00[oool00`000?ooooooo`0Xoooo00<0003oooooool00oooo`030000 oooooooo04coool001_oool200004oooo`030000oooooooo03Goool00`000?ooooooo`0Xoooo00<0 003oooooool01Oooo`030000oooooooo00;oool00`000?ooooooo`0Xoooo00<0003oooooool00ooo o`030000oooooooo01Koool00`000?ooooooo`0coooo000Koooo00<0003oooooool04_ooo`030000 oooooooo02Woool00`000?ooooooo`0loooo00<0003oooooool01oooo`030000oooooooo04;oool0 0`000?ooooooo`0coooo000Koooo00<0003oooooool02oooo`030000oooooooo00coool00`000?oo ooooo`0Qoooo00<0003oooooool0A_ooo`030000oooooooo07Soool001_oool00`000?ooooooo`0; oooo00<0003oooooool03?ooo`030000oooooooo03;oool00`000?ooooooo`0hoooo00<0003ooooo ool05?ooo`030000oooooooo01?oool00`000?ooooooo`0Loooo00<0003oooooool0:Oooo`006ooo o`030000oooooooo04ooool00`000?ooooooo`0=oooo00<0003oooooool0:?ooo`040000oooooooo 00003_ooo`030000oooooooo00;oool00`000?ooooooo`07oooo00<0003oooooool02Oooo`030000 oooooooo01coool010000?ooooooo`0002Soool001_oool00`000?ooooooo`1Ooooo00<0003ooooo ool07Oooo`030000oooooooo00_oool00`000?ooooooo`0?oo o`030000oooooooo04Woool00`000?ooooooo`0Goooo00<0003oooooool07_ooo`030000oooooooo 00ooool00`000?ooooooo`0:oooo00@0003oooooool0000Poooo0008oooo0P0000Coool300000ooo o`800005oooo00<0003oooooool07oooo`030000oooooooo00Goool00`000?ooooooo`0>oooo00<0 003oooooool05oooo`030000oooooooo03[oool00`000?ooooooo`05oooo00<0003oooooool01?oo o`030000oooooooo02Woool00`000?ooooooo`04oooo00@0003oooooool0000_ooo`030000 oooooooo00Ooool00`000?ooooooo`12oooo00<0003oooooool05oooo`006oooo`030000oooooooo 01Ooool00`000?ooooooo`2_oooo00<0003oooooool0=_ooo`006oooo`030000oooooooo03?oool0 0`000?ooooooo`0?oooo00<0003oooooool07oool000[oool010000?ooooooo`00 00;oool010000?ooooooo`0000;oool00`000?ooooooo`3ooooo2?ooo`001oooo`040000oooooooo 00000_ooo`040000oooooooo00000_ooo`040000oooooooo0000ooooo`[oool000Soool200001?oo o`800004oooo0P000?ooool;oooo003ooooo8Oooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -22.9235, \ 0.607629, 1.8727}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 1.73472e-017 0.00618034 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .12361 -12 -4.5 ] [.01131 .12361 0 4.5 ] [.01131 .24721 -12 -4.5 ] [.01131 .24721 0 4.5 ] [.01131 .37082 -12 -4.5 ] [.01131 .37082 0 4.5 ] [.01131 .49443 -12 -4.5 ] [.01131 .49443 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .12361 m .03006 .12361 L s [(20)] .01131 .12361 1 0 Mshowa .02381 .24721 m .03006 .24721 L s [(40)] .01131 .24721 1 0 Mshowa .02381 .37082 m .03006 .37082 L s [(60)] .01131 .37082 1 0 Mshowa .02381 .49443 m .03006 .49443 L s [(80)] .01131 .49443 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(100)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0309 m .02756 .0309 L s .02381 .0618 m .02756 .0618 L s .02381 .09271 m .02756 .09271 L s .02381 .15451 m .02756 .15451 L s .02381 .18541 m .02756 .18541 L s .02381 .21631 m .02756 .21631 L s .02381 .27812 m .02756 .27812 L s .02381 .30902 m .02756 .30902 L s .02381 .33992 m .02756 .33992 L s .02381 .40172 m .02756 .40172 L s .02381 .43262 m .02756 .43262 L s .02381 .46353 m .02756 .46353 L s .02381 .52533 m .02756 .52533 L s .02381 .55623 m .02756 .55623 L s .02381 .58713 m .02756 .58713 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 .61803 Mdot .03651 .61803 Mdot .04286 .61803 Mdot .04921 .12361 Mdot .05556 .61803 Mdot .0619 .12361 Mdot .06825 .61803 Mdot .0746 .61803 Mdot .08095 .24721 Mdot .0873 .20601 Mdot .09365 .0618 Mdot .10635 .0824 Mdot .1127 .18541 Mdot .11905 .30902 Mdot .1254 .12361 Mdot .13175 .0824 Mdot .14444 .16481 Mdot .15079 .30902 Mdot .15714 .29357 Mdot .16349 .28842 Mdot .16984 .2119 Mdot .17619 .02472 Mdot .18254 .10301 Mdot .18889 .45322 Mdot .19524 .04944 Mdot .20159 .18541 Mdot .20794 .16996 Mdot .21429 .61803 Mdot .22063 .19228 Mdot .22698 .12361 Mdot .23333 .03532 Mdot .23968 .01766 Mdot .24603 .10301 Mdot .25238 .27193 Mdot .25873 .14421 Mdot .26508 .0309 Mdot .27143 .01545 Mdot .27778 .16855 Mdot .28413 .10595 Mdot .29048 .18541 Mdot .29683 .13484 Mdot .30317 .15892 Mdot .30952 .30902 Mdot .31587 .04944 Mdot .32222 .02747 Mdot .32857 .07866 Mdot .33492 .06742 Mdot .34127 .10301 Mdot .34762 .09271 Mdot .35397 .02472 Mdot .36032 .03708 Mdot .36667 .01124 Mdot .37302 .0618 Mdot .37937 .08557 Mdot .38571 .14833 Mdot .39206 .03371 Mdot .39841 .11125 Mdot .40476 0 Mdot .41111 .21975 Mdot .41746 .02852 Mdot .42381 .16069 Mdot .43016 .09064 Mdot .43651 0 Mdot .44286 .19777 Mdot .44921 .10043 Mdot .45556 .05768 Mdot .4619 .09271 Mdot .46825 .10301 Mdot .4746 .05705 Mdot .48095 .0618 Mdot .4873 .08725 Mdot .49365 .07998 Mdot .5 .04415 Mdot .50635 .06544 Mdot .5127 .01648 Mdot .51905 .01545 Mdot .5254 .03296 Mdot .53175 0 Mdot .5381 .0618 Mdot .54444 .02181 Mdot .55079 .04807 Mdot .55714 .0309 Mdot .56349 .09271 Mdot .56984 .05855 Mdot .57619 .01454 Mdot .58254 .02181 Mdot .58889 .06798 Mdot .59524 .07725 Mdot .60159 .04363 Mdot .60794 .09271 Mdot .61429 .14833 Mdot .62063 .06544 Mdot .62698 .11588 Mdot .63333 .12361 Mdot .63968 .13133 Mdot .64603 .01952 Mdot .65238 .12855 Mdot .65873 .03253 Mdot .66508 .02354 Mdot .67143 .11372 Mdot .67778 .01177 Mdot .68413 .05912 Mdot .69048 .02809 Mdot .69683 .07156 Mdot .70317 .10934 Mdot .70952 .01124 Mdot .71587 .02354 Mdot .72222 .02943 Mdot .72857 .0215 Mdot .73492 .01612 Mdot .74127 .03605 Mdot .74762 .02247 Mdot .75397 .02575 Mdot .76032 .0206 Mdot .76667 .01545 Mdot .77302 .04495 Mdot .77937 .0215 Mdot .78571 0 Mdot .79206 .06409 Mdot .79841 .0103 Mdot .80476 .03328 Mdot .81111 .07866 Mdot .81746 .02377 Mdot .82381 .0618 Mdot .83016 .01426 Mdot .83651 .00951 Mdot .84286 .07524 Mdot .84921 .04415 Mdot .85556 .00475 Mdot .8619 .01373 Mdot .86825 .00916 Mdot .8746 .00458 Mdot .88095 0 Mdot .8873 .00458 Mdot .89365 .0341 Mdot .9 .04944 Mdot .90635 .01831 Mdot .9127 0 Mdot .91905 .01705 Mdot .9254 .03205 Mdot .93175 .01324 Mdot .9381 .00426 Mdot .94444 .0206 Mdot .95079 .01648 Mdot .95714 .0309 Mdot .96349 .01279 Mdot .96984 .00412 Mdot .97619 0 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooo`030000oooo000000koool00`000?ooooooo`0?oooo00<0003oooooool05?oo o`030000oooooooo00Goool00`000?ooooooo`0>oooo00<0003oooooool01Oooo`030000oooooooo 00Soool01@000?ooooooooooo`000002oooo00<0003oooooool00_ooo`040000oooooooo00004Ooo o`006oooo`030000oooooooo03Goool00`000?ooooooo`13oooo00<0003oooooool01_ooo`030000 oooooooo00Koool00`000?ooooooo`0>oooo00<0003oooooool00_ooo`030000oooooooo00[oool0 10000?ooooooo`0000Coool01@000?ooooooooooo`000003oooo00<0003oooooool01oooo`030000 oooooooo01Coool01@000?ooooooooooo`000005oooo00<0003oool000005?ooo`006oooo`030000 oooooooo02Coool00`000?ooooooo`0Soooo00<0003oooooool01Oooo`030000oooooooo02ooool0 0`000?ooooooo`06oooo00<0003oooooool04oooo`030000oooooooo00[oool010000?ooooooo`00 00Coool01@000?ooo`000?ooo`000003oooo00<0003oooooool01oooo`030000oooooooo01koool0 0`000?ooooooo`0Doooo000Koooo00<0003oooooool09?ooo`030000oooooooo01Coool00`000?oo ooooo`0oooo0P0000Coool200001Oooo`030000oooooooo 04?oool00`000?ooooooo`2loooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`0ioooo00<0003oooooool0a_ooo`006oooo`030000oooooooo03Woool00`000?ooooooo`0N oooo00<0003oooooool0>Oooo`030000oooooooo06Woool001_oool00`000?ooooooo`1Joooo00<0 003oooooool0>Oooo`030000oooooooo06Woool001_oool20000A_ooo`030000oooooooo0;[oool0 01_oool00`000?ooooooo`15oooo00<0003oooooool07?ooo`030000oooooooo09_oool001_oool0 0`000?ooooooo`0Loooo00<0003oooooool0AOooo`030000oooooooo09_oool001_oool00`000?oo ooooo`0Loooo00<0003oooooool03Oooo`030000oooooooo00ooool00`000?ooooooo`31oooo000K oooo00<0003oooooool0;?ooo`030000oooooooo00ooool00`000?ooooooo`31oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 01Coool00`000?ooooooo`0Doooo00<0003oooooool05?ooo`030000oooooooo0;goool001_oool2 00005Oooo`030000oooooooo01Coool00`000?ooooooo`0Doooo00<0003oooooool0_Oooo`006ooo o`030000oooooooo033oool00`000?ooooooo`3?oooo000Koooo00<0003oooooool0oooo00<0003oool000000_ooo`040000oooooooo00001?oo o`030000oooooooo0?ooool3oooo000?oooo0P0000?oool200001Oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo03Soool00`000?ooooooo`37oooo000Koooo00<0003oooooool0>?ooo`030000 oooooooo03oool001_oool00`000?ooooooo`0Ooooo00<0003oooooool0h?ooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`0E oooo00<0003oooooool01_ooo`030000oooooooo02Koool00`000?ooooooo`2hoooo000Koooo0P00 01Koool00`000?ooooooo`06oooo00<0003oooooool09_ooo`030000oooooooo0;Soool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006ooo o`80003ooooo1?ooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0oooo o`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool000goool300001?ooo`800005oooo00<0003oooooool0oooo o`?oool000goool010000?ooooooo`0000;oool010000?ooooooo`0000Coool00`000?ooooooo`3o oooo0oooo`003Oooo`040000oooooooo00000_ooo`040000oooooooo00001?ooo`<0003ooooo0ooo o`003Oooo`<00003oooo00@0003oooooool00004oooo00<0003oooooool0ooooo`?oool000koool0 0`000?ooooooo`02oooo00@0003oooooool00004oooo00<0003oooooool0ooooo`?oool000koool3 00000oooo`800005oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?ooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo0P000?ooool4oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`0W oooo00<0003oooooool0f?ooo`006oooo`030000oooooooo02Ooool00`000?ooooooo`3Hoooo000K oooo00<0003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000>oooo0P00 00Coool200001Oooo`030000oooooooo0?ooool3oooo000=oooo00@0003oooooool00002oooo00@0 003oooooool00004oooo00<0003oooooool0ooooo`?oool000goool010000?ooooooo`0000;oool0 10000?ooooooo`0000Coool30000ooooo`?oool000koool200000oooo`040000oooooooo00001?oo o`030000oooooooo0?ooool3oooo000=oooo00@0003oooooool00002oooo00@0003oooooool00004 oooo00<0003oooooool0ooooo`?oool000koool200001?ooo`800005oooo00<0003oooooool0oooo o`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003o oooo1?ooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo0P000?ooool4oooo000Koooo00<0003oooooool0ooooo`?oool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0oooo o`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo0007 oooo1@0000;oool200001?ooo`800005oooo00<0003oooooool0ooooo`?oool000Woool01@000?oo ooooooooo`000002oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`8000001?ooo`00 0?ooo`0000;oool01P000?ooooooo`000?ooo`0002?oool00`000?ooooooo`3Aoooo0009oooo00D0 003oooooooooool000000_ooo`040000oooooooo00000_ooo`030000oooooooo00;oool4000000Go ool0003oooooool000000_ooo`030000oooo000002?oool00`000?ooooooo`3Aoooo0009oooo00D0 003oooooooooool000000_ooo`040000oooooooo00000_ooo`030000oooooooo0?ooool8oooo0009 oooo00D0003oooooooooool000000_ooo`040000oooooooo00000_ooo`030000oooooooo0?ooool8 oooo0008oooo0P0000Coool200001?ooo`80003ooooo2oooo`00ooooob7oool00001\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -7.64114, \ 0.607629, 0.624232}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 -2.60209e-017 0.00206011 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .10301 -12 -4.5 ] [.01131 .10301 0 4.5 ] [.01131 .20601 -18 -4.5 ] [.01131 .20601 0 4.5 ] [.01131 .30902 -18 -4.5 ] [.01131 .30902 0 4.5 ] [.01131 .41202 -18 -4.5 ] [.01131 .41202 0 4.5 ] [.01131 .51503 -18 -4.5 ] [.01131 .51503 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .10301 m .03006 .10301 L s [(50)] .01131 .10301 1 0 Mshowa .02381 .20601 m .03006 .20601 L s [(100)] .01131 .20601 1 0 Mshowa .02381 .30902 m .03006 .30902 L s [(150)] .01131 .30902 1 0 Mshowa .02381 .41202 m .03006 .41202 L s [(200)] .01131 .41202 1 0 Mshowa .02381 .51503 m .03006 .51503 L s [(250)] .01131 .51503 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(300)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0206 m .02756 .0206 L s .02381 .0412 m .02756 .0412 L s .02381 .0618 m .02756 .0618 L s .02381 .0824 m .02756 .0824 L s .02381 .12361 m .02756 .12361 L s .02381 .14421 m .02756 .14421 L s .02381 .16481 m .02756 .16481 L s .02381 .18541 m .02756 .18541 L s .02381 .22661 m .02756 .22661 L s .02381 .24721 m .02756 .24721 L s .02381 .26781 m .02756 .26781 L s .02381 .28842 m .02756 .28842 L s .02381 .32962 m .02756 .32962 L s .02381 .35022 m .02756 .35022 L s .02381 .37082 m .02756 .37082 L s .02381 .39142 m .02756 .39142 L s .02381 .43262 m .02756 .43262 L s .02381 .45322 m .02756 .45322 L s .02381 .47383 m .02756 .47383 L s .02381 .49443 m .02756 .49443 L s .02381 .53563 m .02756 .53563 L s .02381 .55623 m .02756 .55623 L s .02381 .57683 m .02756 .57683 L s .02381 .59743 m .02756 .59743 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 0 Mdot .03651 .12361 Mdot .04286 0 Mdot .04921 .24721 Mdot .05556 .15451 Mdot .0619 .37082 Mdot .06825 0 Mdot .0746 .16481 Mdot .08095 .27812 Mdot .0873 .20601 Mdot .09365 .13597 Mdot .1 .24721 Mdot .10635 .26781 Mdot .1127 .21631 Mdot .1254 .32962 Mdot .13175 .26266 Mdot .1381 .27812 Mdot .14444 .29357 Mdot .15079 .61803 Mdot .15714 .32447 Mdot .16349 .22661 Mdot .18254 .30902 Mdot .18889 .32138 Mdot .19524 .20859 Mdot .20159 .3461 Mdot .20794 .35846 Mdot .21429 .37082 Mdot .22063 .38318 Mdot .22698 .21975 Mdot .23333 .33992 Mdot .23968 .35022 Mdot .24603 .21631 Mdot .25238 .31785 Mdot .25873 .38112 Mdot .26508 .29357 Mdot .27143 .40172 Mdot .27778 .27468 Mdot .28413 .42232 Mdot .29048 .37082 Mdot .29683 .29528 Mdot .30317 .33992 Mdot .30952 .55623 Mdot .31587 .25845 Mdot .32222 .26407 Mdot .32857 .29666 Mdot .33492 .43262 Mdot .34127 .28092 Mdot .34762 .35022 Mdot .35397 .32138 Mdot .36032 .29778 Mdot .36667 .41717 Mdot .37302 .26148 Mdot .37937 .3461 Mdot .38571 .35228 Mdot .39206 .32587 Mdot .39841 .24309 Mdot .40476 .28525 Mdot .41111 .34273 Mdot .41746 .34835 Mdot .42381 .35396 Mdot .43016 .49443 Mdot .43651 .40172 Mdot .44286 .29136 Mdot .44921 .37644 Mdot .45556 .35022 Mdot .4619 .25085 Mdot .46825 .39329 Mdot .4746 .29254 Mdot .48095 .24721 Mdot .4873 .26539 Mdot .49365 .38112 Mdot .5 .24396 Mdot .50635 .24721 Mdot .5127 .33992 Mdot .51905 .26781 Mdot .5254 .2872 Mdot .53175 .29084 Mdot .5381 .26348 Mdot .54444 .31674 Mdot .55079 .25648 Mdot .55714 .27324 Mdot .56349 .35022 Mdot .56984 .27974 Mdot .57619 .29872 Mdot .58254 .28625 Mdot .58889 .32356 Mdot .59524 .34764 Mdot .60159 .40172 Mdot .60794 .24721 Mdot .61429 .35923 Mdot .62063 .32275 Mdot .62698 .32618 Mdot .63333 .31227 Mdot .63968 .28547 Mdot .64603 .31878 Mdot .65238 .30593 Mdot .65873 .28092 Mdot .66508 .32853 Mdot .67143 .30019 Mdot .67778 .35365 Mdot .68413 .33829 Mdot .69048 .30902 Mdot .69683 .28483 Mdot .70317 .26452 Mdot .70952 .29021 Mdot .71587 .35456 Mdot .72222 .30902 Mdot .72857 .26385 Mdot .73492 .3461 Mdot .74127 .27935 Mdot .74762 .29357 Mdot .75397 .29614 Mdot .76032 .29872 Mdot .76667 .28924 Mdot .77302 .31708 Mdot .77937 .29418 Mdot .78571 .30902 Mdot .79206 .28762 Mdot .79841 .3016 Mdot .80476 .29238 Mdot .81111 .3332 Mdot .81746 .32189 Mdot .82381 .26853 Mdot .83016 .2907 Mdot .83651 .34395 Mdot .84286 .31891 Mdot .84921 .29757 Mdot .85556 .32385 Mdot .8619 .28131 Mdot .86825 .29357 Mdot .8746 .28557 Mdot .88095 .30902 Mdot .8873 .30019 Mdot .89365 .3136 Mdot .9 .3046 Mdot .90635 .31817 Mdot .9127 .29836 Mdot .91905 .30049 Mdot .9254 .30262 Mdot .93175 .32733 Mdot .9381 .30689 Mdot .94444 .30902 Mdot .95079 .30078 Mdot .95714 .30284 Mdot .96349 .3049 Mdot .96984 .30696 Mdot .97619 .30902 Mdot .5 Mabswid .02381 .37082 m .06244 .37082 L .10458 .37082 L .14415 .37082 L .18221 .37082 L .22272 .37082 L .26171 .37082 L .30316 .37082 L .34309 .37082 L .3815 .37082 L .42237 .37082 L .46172 .37082 L .49955 .37082 L .53984 .37082 L .57861 .37082 L .61984 .37082 L .65954 .37082 L .69774 .37082 L .73838 .37082 L .77751 .37082 L .81909 .37082 L .85916 .37082 L .89771 .37082 L .93871 .37082 L .97619 .37082 L s .02381 .24721 m .06244 .24721 L .10458 .24721 L .14415 .24721 L .18221 .24721 L .22272 .24721 L .26171 .24721 L .30316 .24721 L .34309 .24721 L .3815 .24721 L .42237 .24721 L .46172 .24721 L .49955 .24721 L .53984 .24721 L .57861 .24721 L .61984 .24721 L .65954 .24721 L .69774 .24721 L .73838 .24721 L .77751 .24721 L .81909 .24721 L .85916 .24721 L .89771 .24721 L .93871 .24721 L .97619 .24721 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooo0P0000Coool200001Oooo`030000oooooooo0?ooool3oooo000=oooo00@0003ooooo ool00002oooo00@0003oooooool00004oooo00<0003oooooool0ooooo`?oool0013oool010000?oo ooooo`0000;oool00`000?ooooooo`02oooo0`000?ooool3oooo000>oooo0P0000?oool010000?oo ooooo`0000Coool00`000?ooooooo`3ooooo0oooo`003_ooo`030000oooooooo00;oool010000?oo ooooo`0000Coool00`000?ooooooo`3ooooo0oooo`003_ooo`<00003oooo0P0000Goool00`000?oo ooooo`3ooooo0oooo`006oooo`040000oooooooo0000ooooo`;oool001_oool2000000?oool0003o ool0ooooo`7oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool03oooo`030000oooooooo0?3oool001_oool00`000?ooooooo`0? oooo00<0003oooooool0l?ooo`006oooo`80003ooooo1?ooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool01Oooo`030000oooooooo0?[oool001_oool00`000?ooooooo`05 oooo00<0003oooooool0n_ooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool02_ooo`030000oooooooo0?Goool001_oool200002oooo`030000oooooooo0?Goool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?ooo`006ooo o`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool000Ooool500000_oo o`800004oooo0P0000Goool00`000?ooooooo`3ooooo0oooo`002Oooo`050000oooooooooooo0000 00;oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0003oooooool0ooooo`?oool0 00Woool01@000?ooooooooooo`000002oooo00@0003oooooool00002oooo00<0003oooooool00_oo o`<0000=oooo00<0003oooooool06Oooo`030000oooooooo0=Koool000Woool01@000?oooooooooo o`000002oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`030000oooooooo00goool0 0`000?ooooooo`0Ioooo00<0003oooooool0e_ooo`002Oooo`050000oooooooooooo000000;oool0 10000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0003oooooool05?ooo`030000oooooooo 01ooool00`000?ooooooo`39oooo0008oooo0P0000Coool200001?ooo`800005oooo00<0003ooooo ool05?ooo`030000oooooooo01[oool00`000?ooooooo`02oooo00<0003oooooool0bOooo`006ooo o`030000oooooooo037oool00`000?ooooooo`3>oooo000Koooo00<0003oooooool08Oooo`030000 oooooooo0=koool001_oool200008_ooo`030000oooooooo0=koool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0G_ooo`030000 oooooooo0:7oool001_oool00`000?ooooooo`03oooo00<0003oooooool02_ooo`030000oooooooo 04_oool00`000?ooooooo`0Boooo00<0003oooooool00_ooo`030000oooo000001Woool00`000?oo ooooo`1[oooo000Koooon00000goool001_oool00`000?ooooooo`1^oooo00<0003oooooool0TOoo o`006oooo`030000oooooooo04Soool00`000?ooooooo`0joooo00<0003oooooool0N_ooo`006ooo o`030000oooooooo01Woool00`000?ooooooo`0/oooo00<0003oooooool03?ooo`030000oooooooo 02_oool00`000?ooooooo`1joooo000Koooo00<0003oooooool06Oooo`030000oooooooo02koool0 0`000?ooooooo`0:oooo00<0003oooooool06oooo`030000oooooooo00[oool00`000?ooooooo`0X oooo00<0003oooooool00oooo`030000oooooooo04coool001_oool200004oooo`030000oooooooo 03Goool00`000?ooooooo`0Xoooo00<0003oooooool01Oooo`030000oooooooo00;oool00`000?oo ooooo`0Xoooo00<0003oooooool00oooo`030000oooooooo01Koool00`000?ooooooo`0coooo000K oooo00<0003oooooool04_ooo`030000oooooooo02Woool00`000?ooooooo`0loooo00<0003ooooo ool01oooo`030000oooooooo04;oool00`000?ooooooo`0coooo000Koooo00<0003oooooool02ooo o`030000oooooooo00coool00`000?ooooooo`0Qoooo00<0003oooooool0A_ooo`030000oooooooo 07Soool001_oool00`000?ooooooo`0;oooo00<0003oooooool03?ooo`030000oooooooo03;oool0 0`000?ooooooo`0hoooo00<0003oooooool05?ooo`030000oooooooo01?oool00`000?ooooooo`0L oooo00<0003oooooool0:Oooo`006oooo`030000oooooooo04ooool00`000?ooooooo`0=oooo00<0 003oooooool0:?ooo`040000oooooooo00003_ooo`030000oooooooo00;oool00`000?ooooooo`07 oooo00<0003oooooool02Oooo`030000oooooooo01coool010000?ooooooo`0002Soool001_oool0 0`000?ooooooo`1Ooooo00<0003oooooool07Oooo`030000oooooooo00_oool00`000?ooooooo`0< oooo00<0003oooooool03?ooo`030000oooooooo00ooool00`000?ooooooo`04oooo00<0003ooooo ool04_ooo`030000oooooooo02Koool001_oool200007Oooo`030000oooooooo01coool00`000?oo ooooo`0[oooo00<0003oooooool01Oooo`030000oooooooo00_oool20000;Oooo`030000oooooooo 00Ooool00`000?ooooooo`02oooo00<0003oooooool01?ooo`040000oooooooo00001_ooo`030000 oooooooo00Koool00`000?ooooooo`0Xoooo000Koooo00<0003oooooool07?ooo`030000oooooooo 01coool00`000?ooooooo`05oooo00<0003oooooool01_ooo`030000oooooooo00Goool00`000?oo ooooo`0Boooo00<0003oooooool01Oooo`030000oooooooo00coool00`000?ooooooo`0[oooo00<0 003oooooool01oooo`030000oooo000000Goool00`000?ooooooo`04oooo00<0003oooooool01?oo o`030000oooooooo00;oool01@000?ooooooooooo`00000Zoooo000Koooo00<0003oooooool0@ooo o`030000oooooooo00Koool00`000?ooooooo`05oooo00<0003oooooool0=Oooo`030000oooooooo 01Goool00`000?ooooooo`0Coooo00<0003oool000000oooo`030000oooooooo00;oool00`000?oo ooooo`0;oooo00<0003oooooool01_ooo`030000oooooooo00Coool00`000?ooo`000007oooo00<0 003oooooool04_ooo`001oooo`D00002oooo0P0000Coool200001Oooo`030000oooooooo08coool0 0`000?ooooooo`0Eoooo00<0003oooooool05Oooo`030000oooooooo00Koool00`000?ooooooo`0D oooo00D0003oooooooooool000000_ooo`040000oooo000000001_ooo`040000oooo000000004Ooo o`002Oooo`050000oooooooooooo000000;oool010000?ooooooo`0000;oool00`000?ooooooo`02 oooo00<0003oooooool09_ooo`030000oooooooo07Ooool00`000?ooooooo`06oooo00<0003ooooo ool01_ooo`030000oooooooo00goool00`000?ooooooo`0Foooo00<0003oooooool00_ooo`030000 oooooooo00?oool010000?ooooooooooo`800003oooo0P000003oooo0000000000koool000Woool0 0`000?ooooooo`04oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`<0000Voooo00<0 003oooooool0L_ooo`030000oooooooo00;oool00`000?ooooooo`06oooo00<0003oooooool01_oo o`030000oooooooo00goool00`000?ooooooo`0Foooo00<0003oooooool03?ooo`800006oooo0P00 00koool000Woool00`000?ooooooo`02oooo0P0000?oool010000?ooooooo`0000Coool00`000?oo ooooo`24oooo00<0003oooooool05?ooo`030000oooooooo027oool00`000?ooooooo`0Loooo00<0 003oooooool08Oooo`002Oooo`030000oooooooo00;oool00`000?ooooooo`02oooo00@0003ooooo ool00004oooo00<0003oooooool0>?ooo`030000oooooooo04Woool00`000?ooooooo`0Goooo00<0 003oooooool07_ooo`030000oooooooo00ooool00`000?ooooooo`0:oooo00@0003oooooool0000P oooo0008oooo0P0000Coool300000oooo`800005oooo00<0003oooooool07oooo`030000oooooooo 00Goool00`000?ooooooo`0>oooo00<0003oooooool05oooo`030000oooooooo03[oool00`000?oo ooooo`05oooo00<0003oooooool01?ooo`030000oooooooo02Woool00`000?ooooooo`04oooo00@0 003oooooool0000_ooo`030000oooooooo00Ooool00`000?ooooooo`12oooo00<0003ooooo ool05oooo`006oooo`030000oooooooo01Ooool00`000?ooooooo`2_oooo00<0003oooooool0=_oo o`006oooo`030000oooooooo03?oool00`000?ooooooo`0?oooo00<0003oooooool07oool000[oool010000?ooooooo`0000;oool010000?ooooooo`0000;oool0 0`000?ooooooo`3ooooo2?ooo`001oooo`040000oooooooo00000_ooo`040000oooooooo00000_oo o`040000oooooooo0000ooooo`[oool000Soool200001?ooo`800004oooo0P000?ooool;oooo003o oooo8Oooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -22.9235, \ 0.607629, 1.8727}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 1.73472e-017 0.00618034 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .12361 -12 -4.5 ] [.01131 .12361 0 4.5 ] [.01131 .24721 -12 -4.5 ] [.01131 .24721 0 4.5 ] [.01131 .37082 -12 -4.5 ] [.01131 .37082 0 4.5 ] [.01131 .49443 -12 -4.5 ] [.01131 .49443 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .12361 m .03006 .12361 L s [(20)] .01131 .12361 1 0 Mshowa .02381 .24721 m .03006 .24721 L s [(40)] .01131 .24721 1 0 Mshowa .02381 .37082 m .03006 .37082 L s [(60)] .01131 .37082 1 0 Mshowa .02381 .49443 m .03006 .49443 L s [(80)] .01131 .49443 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(100)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0309 m .02756 .0309 L s .02381 .0618 m .02756 .0618 L s .02381 .09271 m .02756 .09271 L s .02381 .15451 m .02756 .15451 L s .02381 .18541 m .02756 .18541 L s .02381 .21631 m .02756 .21631 L s .02381 .27812 m .02756 .27812 L s .02381 .30902 m .02756 .30902 L s .02381 .33992 m .02756 .33992 L s .02381 .40172 m .02756 .40172 L s .02381 .43262 m .02756 .43262 L s .02381 .46353 m .02756 .46353 L s .02381 .52533 m .02756 .52533 L s .02381 .55623 m .02756 .55623 L s .02381 .58713 m .02756 .58713 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 .61803 Mdot .03651 .61803 Mdot .04286 .61803 Mdot .04921 .12361 Mdot .05556 .61803 Mdot .0619 .12361 Mdot .06825 .61803 Mdot .0746 .61803 Mdot .08095 .24721 Mdot .0873 .20601 Mdot .09365 .0618 Mdot .10635 .0824 Mdot .1127 .18541 Mdot .11905 .30902 Mdot .1254 .12361 Mdot .13175 .0824 Mdot .14444 .16481 Mdot .15079 .30902 Mdot .15714 .29357 Mdot .16349 .28842 Mdot .16984 .2119 Mdot .17619 .02472 Mdot .18254 .10301 Mdot .18889 .45322 Mdot .19524 .04944 Mdot .20159 .18541 Mdot .20794 .16996 Mdot .21429 .61803 Mdot .22063 .19228 Mdot .22698 .12361 Mdot .23333 .03532 Mdot .23968 .01766 Mdot .24603 .10301 Mdot .25238 .27193 Mdot .25873 .14421 Mdot .26508 .0309 Mdot .27143 .01545 Mdot .27778 .16855 Mdot .28413 .10595 Mdot .29048 .18541 Mdot .29683 .13484 Mdot .30317 .15892 Mdot .30952 .30902 Mdot .31587 .04944 Mdot .32222 .02747 Mdot .32857 .07866 Mdot .33492 .06742 Mdot .34127 .10301 Mdot .34762 .09271 Mdot .35397 .02472 Mdot .36032 .03708 Mdot .36667 .01124 Mdot .37302 .0618 Mdot .37937 .08557 Mdot .38571 .14833 Mdot .39206 .03371 Mdot .39841 .11125 Mdot .40476 0 Mdot .41111 .21975 Mdot .41746 .02852 Mdot .42381 .16069 Mdot .43016 .09064 Mdot .43651 0 Mdot .44286 .19777 Mdot .44921 .10043 Mdot .45556 .05768 Mdot .4619 .09271 Mdot .46825 .10301 Mdot .4746 .05705 Mdot .48095 .0618 Mdot .4873 .08725 Mdot .49365 .07998 Mdot .5 .04415 Mdot .50635 .06544 Mdot .5127 .01648 Mdot .51905 .01545 Mdot .5254 .03296 Mdot .53175 0 Mdot .5381 .0618 Mdot .54444 .02181 Mdot .55079 .04807 Mdot .55714 .0309 Mdot .56349 .09271 Mdot .56984 .05855 Mdot .57619 .01454 Mdot .58254 .02181 Mdot .58889 .06798 Mdot .59524 .07725 Mdot .60159 .04363 Mdot .60794 .09271 Mdot .61429 .14833 Mdot .62063 .06544 Mdot .62698 .11588 Mdot .63333 .12361 Mdot .63968 .13133 Mdot .64603 .01952 Mdot .65238 .12855 Mdot .65873 .03253 Mdot .66508 .02354 Mdot .67143 .11372 Mdot .67778 .01177 Mdot .68413 .05912 Mdot .69048 .02809 Mdot .69683 .07156 Mdot .70317 .10934 Mdot .70952 .01124 Mdot .71587 .02354 Mdot .72222 .02943 Mdot .72857 .0215 Mdot .73492 .01612 Mdot .74127 .03605 Mdot .74762 .02247 Mdot .75397 .02575 Mdot .76032 .0206 Mdot .76667 .01545 Mdot .77302 .04495 Mdot .77937 .0215 Mdot .78571 0 Mdot .79206 .06409 Mdot .79841 .0103 Mdot .80476 .03328 Mdot .81111 .07866 Mdot .81746 .02377 Mdot .82381 .0618 Mdot .83016 .01426 Mdot .83651 .00951 Mdot .84286 .07524 Mdot .84921 .04415 Mdot .85556 .00475 Mdot .8619 .01373 Mdot .86825 .00916 Mdot .8746 .00458 Mdot .88095 0 Mdot .8873 .00458 Mdot .89365 .0341 Mdot .9 .04944 Mdot .90635 .01831 Mdot .9127 0 Mdot .91905 .01705 Mdot .9254 .03205 Mdot .93175 .01324 Mdot .9381 .00426 Mdot .94444 .0206 Mdot .95079 .01648 Mdot .95714 .0309 Mdot .96349 .01279 Mdot .96984 .00412 Mdot .97619 0 Mdot .5 Mabswid .02381 .12361 m .06244 .12361 L .10458 .12361 L .14415 .12361 L .18221 .12361 L .22272 .12361 L .26171 .12361 L .30316 .12361 L .34309 .12361 L .3815 .12361 L .42237 .12361 L .46172 .12361 L .49955 .12361 L .53984 .12361 L .57861 .12361 L .61984 .12361 L .65954 .12361 L .69774 .12361 L .73838 .12361 L .77751 .12361 L .81909 .12361 L .85916 .12361 L .89771 .12361 L .93871 .12361 L .97619 .12361 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooo`030000oooo000000koool00`000?ooooooo`0?oooo00<0003oooooool05?oo o`030000oooooooo00Goool00`000?ooooooo`0>oooo00<0003oooooool01Oooo`030000oooooooo 00Soool01@000?ooooooooooo`000002oooo00<0003oooooool00_ooo`040000oooooooo00004Ooo o`006oooo`030000oooooooo03Goool00`000?ooooooo`13oooo00<0003oooooool01_ooo`030000 oooooooo00Koool00`000?ooooooo`0>oooo00<0003oooooool00_ooo`030000oooooooo00[oool0 10000?ooooooo`0000Coool01@000?ooooooooooo`000003oooo00<0003oooooool01oooo`030000 oooooooo01Coool01@000?ooooooooooo`000005oooo00<0003oool000005?ooo`006oooo`030000 oooooooo02Coool00`000?ooooooo`0Soooo00<0003oooooool01Oooo`030000oooooooo02ooool0 0`000?ooooooo`06oooo00<0003oooooool04oooo`030000oooooooo00[oool010000?ooooooo`00 00Coool01@000?ooo`000?ooo`000003oooo00<0003oooooool01oooo`030000oooooooo01koool0 0`000?ooooooo`0Doooo000Koooo00<0003oooooool09?ooo`030000oooooooo01Coool00`000?oo ooooo`0oooo0P0000Coool200001Oooo`030000oooooooo04?oool0 0`000?ooooooo`2loooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`0i oooo00<0003oooooool0a_ooo`006oooo`030000oooooooo03Woool00`000?ooooooo`0Noooo00<0 003oooooool0>Oooo`030000oooooooo06Woool001_oool00`000?ooooooo`1Joooo00<0003ooooo ool0>Oooo`030000oooooooo06Woool001_oool20000A_ooo`030000oooooooo0;[oool001_oool0 0`000?ooooooo`15oooo00<0003oooooool07?ooo`030000oooooooo09_oool001_oool00`000?oo ooooo`0Loooo00<0003oooooool0AOooo`030000oooooooo09_oool001_oool00`000?ooooooo`0L oooo00<0003oooooool03Oooo`030000oooooooo00ooool00`000?ooooooo`31oooo000Koooo00<0 003oooooool0;?ooo`030000oooooooo00ooool00`000?ooooooo`31oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo01Coool0 0`000?ooooooo`0Doooo00<0003oooooool05?ooo`030000oooooooo0;goool001_oool200005Ooo o`030000oooooooo01Coool00`000?ooooooo`0Doooo00<0003oooooool0_Oooo`006oooo`030000 oooooooo033oool00`000?ooooooo`3?oooo000Koooo00<0003oooooool0oooo00<0003oool000000_ooo`040000oooooooo00001?ooo`030000 oooooooo0?ooool3oooo000?oooo0P0000?oool200001Oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000 oooooooo03Soool00`000?ooooooo`37oooo000Koooo00<0003oooooool0>?ooo`030000oooooooo 03oool001_oool00`000?ooooooo`0Ooooo00<0003oooooool0h?ooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`0Eoooo00<0 003oooooool01_ooo`030000oooooooo02Koool00`000?ooooooo`2hoooo000Koooo0P0001Koool0 0`000?ooooooo`06oooo00<0003oooooool09_ooo`030000oooooooo0;Soool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0oooo o`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003o oooo1?ooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool000goool300001?ooo`800005oooo00<0003oooooool0ooooo`?oool0 00goool010000?ooooooo`0000;oool010000?ooooooo`0000Coool00`000?ooooooo`3ooooo0ooo o`003Oooo`040000oooooooo00000_ooo`040000oooooooo00001?ooo`<0003ooooo0oooo`003Ooo o`<00003oooo00@0003oooooool00004oooo00<0003oooooool0ooooo`?oool000koool00`000?oo ooooo`02oooo00@0003oooooool00004oooo00<0003oooooool0ooooo`?oool000koool300000ooo o`800005oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`80003ooooo1?ooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo0P000?ooool4oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`0Woooo00<0 003oooooool0f?ooo`006oooo`030000oooooooo02Ooool00`000?ooooooo`3Hoooo000Koooo00<0 003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000>oooo0P0000Coool2 00001Oooo`030000oooooooo0?ooool3oooo000=oooo00@0003oooooool00002oooo00@0003ooooo ool00004oooo00<0003oooooool0ooooo`?oool000goool010000?ooooooo`0000;oool010000?oo ooooo`0000Coool30000ooooo`?oool000koool200000oooo`040000oooooooo00001?ooo`030000 oooooooo0?ooool3oooo000=oooo00@0003oooooool00002oooo00@0003oooooool00004oooo00<0 003oooooool0ooooo`?oool000koool200001?ooo`800005oooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?oo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo0P000?ooool4oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0oooo o`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo0007oooo1@00 00;oool200001?ooo`800005oooo00<0003oooooool0ooooo`?oool000Woool01@000?oooooooooo o`000002oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`8000001?ooo`000?ooo`00 00;oool01P000?ooooooo`000?ooo`0002?oool00`000?ooooooo`3Aoooo0009oooo00D0003ooooo ooooool000000_ooo`040000oooooooo00000_ooo`030000oooooooo00;oool4000000Goool0003o ooooool000000_ooo`030000oooo000002?oool00`000?ooooooo`3Aoooo0009oooo00D0003ooooo ooooool000000_ooo`040000oooooooo00000_ooo`030000oooooooo0?ooool8oooo0009oooo00D0 003oooooooooool000000_ooo`040000oooooooo00000_ooo`030000oooooooo0?ooool8oooo0008 oooo0P0000Coool200001?ooo`80003ooooo2oooo`00ooooob7oool00001\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -7.64114, \ 0.607629, 0.624232}}] }, Open ]] }, Open ]], Cell[TextData[{ StyleBox["\tDoes the order of the catch appear to make a significant \ difference in accuracy of the prediction?\n\t\n\t Notice that each data point \ is a single guess for the population measurement, and can vary quite a bit \ due to the dependence on probability.\nWe might get a more consistent picture \ if we tried, say, 10 catches at every point and averaged the results. To do \ so, we will need to define a ", FontSize->14], StyleBox["Mean", "Input", FontSize->14], StyleBox[" function, which takes a list (", FontSize->14], StyleBox["data", "Input", FontSize->14], StyleBox["), adds up the elements (", FontSize->14], StyleBox["Apply[Plus,...]", "Input", FontSize->14], StyleBox[") and divides by the number of elements (", FontSize->14], StyleBox["Length[data]", "Input", FontSize->14], StyleBox["). [Note this function is also available in the ", FontSize->14], StyleBox["Mathematica", FontSize->14, FontSlant->"Italic"], StyleBox[" DescriptiveStatistics package].", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Mean[data_]\ := \ N[Apply[Plus, data]/Length[data]];\)\), "\[IndentingNewLine]", \(Mean[{1, 2, 3, 4}]\)}], "Input"], Cell[BoxData[ \(2.5`\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tTo average 10 guesses, we make a ", FontSize->14], StyleBox["Table", "Input", FontSize->14], StyleBox[" with 10 values from ", FontSize->14], StyleBox["GuessPop", "Input", FontSize->14], StyleBox[" and apply ", FontSize->14], StyleBox["Mean", "Input", FontSize->14], StyleBox[".", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Mean[Table[\(GuessPop[150, 30, 5]\)[\([1]\)], {10}]]\)], "Input"], Cell[BoxData[ \(82.5`\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["\tIf we use these average values in the catch tables instead, we \ find that the data points don't vary nearly as much. Note, however, that the \ simulation takes a fairly long time, as we are making 150*10 = 1500 guesses, \ each of which requires a run of our ", FontSize->14], StyleBox["GuessPop", "Input", FontSize->14], StyleBox[" function! (Note: the following is a second catch simulation).", FontSize->14] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(PopSize\ = \ 150;\)\), "\[IndentingNewLine]", \(\(Est2Catch\ = \[IndentingNewLine]Table[\[IndentingNewLine]Mean[ Table[\(GuessPop[PopSize, 30, i]\)[\([1]\)], {10}]], {i, PopSize}];\)\), "\[IndentingNewLine]", \(\(Err2Catch\ = \[IndentingNewLine]Table[\[IndentingNewLine]Mean[ Table[\(GuessPop[PopSize, 30, i]\)[\([3]\)], {10}]], {i, PopSize}];\)\), "\[IndentingNewLine]", \(\(PlotEst\ = \ ListPlot[Est2Catch, PlotRange \[Rule] {0, 2*PopSize}];\)\), "\[IndentingNewLine]", \(\(PlotErr\ = \ ListPlot[Err2Catch, PlotRange \[Rule] {0, 100}];\)\), "\[IndentingNewLine]", \(\(Show[PlotEst, EstHi20, EstLo20];\)\), "\n", \(\(Show[PlotErr, Err20];\)\)}], "Input"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 -2.60209e-017 0.00206011 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .10301 -12 -4.5 ] [.01131 .10301 0 4.5 ] [.01131 .20601 -18 -4.5 ] [.01131 .20601 0 4.5 ] [.01131 .30902 -18 -4.5 ] [.01131 .30902 0 4.5 ] [.01131 .41202 -18 -4.5 ] [.01131 .41202 0 4.5 ] [.01131 .51503 -18 -4.5 ] [.01131 .51503 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .10301 m .03006 .10301 L s [(50)] .01131 .10301 1 0 Mshowa .02381 .20601 m .03006 .20601 L s [(100)] .01131 .20601 1 0 Mshowa .02381 .30902 m .03006 .30902 L s [(150)] .01131 .30902 1 0 Mshowa .02381 .41202 m .03006 .41202 L s [(200)] .01131 .41202 1 0 Mshowa .02381 .51503 m .03006 .51503 L s [(250)] .01131 .51503 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(300)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0206 m .02756 .0206 L s .02381 .0412 m .02756 .0412 L s .02381 .0618 m .02756 .0618 L s .02381 .0824 m .02756 .0824 L s .02381 .12361 m .02756 .12361 L s .02381 .14421 m .02756 .14421 L s .02381 .16481 m .02756 .16481 L s .02381 .18541 m .02756 .18541 L s .02381 .22661 m .02756 .22661 L s .02381 .24721 m .02756 .24721 L s .02381 .26781 m .02756 .26781 L s .02381 .28842 m .02756 .28842 L s .02381 .32962 m .02756 .32962 L s .02381 .35022 m .02756 .35022 L s .02381 .37082 m .02756 .37082 L s .02381 .39142 m .02756 .39142 L s .02381 .43262 m .02756 .43262 L s .02381 .45322 m .02756 .45322 L s .02381 .47383 m .02756 .47383 L s .02381 .49443 m .02756 .49443 L s .02381 .53563 m .02756 .53563 L s .02381 .55623 m .02756 .55623 L s .02381 .57683 m .02756 .57683 L s .02381 .59743 m .02756 .59743 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 .00618 Mdot .03651 .0309 Mdot .04286 .05562 Mdot .04921 .13185 Mdot .05556 .15451 Mdot .0619 .19777 Mdot .06825 .24515 Mdot .0746 .19365 Mdot .08095 .27812 Mdot .0873 .28533 Mdot .09365 .41017 Mdot .1 .33621 Mdot .10635 .50215 Mdot .1127 .274 Mdot .11905 .42335 Mdot .1254 .32962 Mdot .13175 .48155 Mdot .1381 .3589 Mdot .14444 .34473 Mdot .15079 .38848 Mdot .15714 .28121 Mdot .16349 .29686 Mdot .16984 .40038 Mdot .17619 .4969 Mdot .18254 .29099 Mdot .18889 .33496 Mdot .19524 .33738 Mdot .20159 .34631 Mdot .20794 .34893 Mdot .21429 .45646 Mdot .22063 .32669 Mdot .22698 .38142 Mdot .23333 .37496 Mdot .23968 .32695 Mdot .24603 .38061 Mdot .25238 .54176 Mdot .25873 .34411 Mdot .26508 .40904 Mdot .27143 .35993 Mdot .27778 .34698 Mdot .28413 .36923 Mdot .29048 .32058 Mdot .29683 .30255 Mdot .30317 .32795 Mdot .30952 .3717 Mdot .31587 .27458 Mdot .32222 .34178 Mdot .32857 .3526 Mdot .33492 .31474 Mdot .34127 .34082 Mdot .34762 .35847 Mdot .35397 .33274 Mdot .36032 .3311 Mdot .36667 .35 Mdot .37302 .31491 Mdot .37937 .28055 Mdot .38571 .33985 Mdot .39206 .33444 Mdot .39841 .32244 Mdot .40476 .31552 Mdot .41111 .32184 Mdot .41746 .34497 Mdot .42381 .32647 Mdot .43016 .3039 Mdot .43651 .31471 Mdot .44286 .34456 Mdot .44921 .31297 Mdot .45556 .33854 Mdot .4619 .31626 Mdot .46825 .31659 Mdot .4746 .31874 Mdot .48095 .32306 Mdot .4873 .28725 Mdot .49365 .35273 Mdot .5 .30312 Mdot .50635 .30783 Mdot .5127 .29676 Mdot .51905 .32933 Mdot .5254 .36197 Mdot .53175 .32134 Mdot .5381 .29731 Mdot .54444 .31659 Mdot .55079 .32757 Mdot .55714 .28458 Mdot .56349 .31709 Mdot .56984 .31298 Mdot .57619 .31267 Mdot .58254 .29314 Mdot .58889 .34328 Mdot .59524 .2979 Mdot .60159 .32746 Mdot .60794 .32739 Mdot .61429 .29969 Mdot .62063 .31704 Mdot .62698 .32614 Mdot .63333 .31242 Mdot .63968 .31016 Mdot .64603 .3177 Mdot .65238 .34233 Mdot .65873 .30513 Mdot .66508 .32571 Mdot .67143 .32332 Mdot .67778 .31181 Mdot .68413 .31412 Mdot .69048 .33437 Mdot .69683 .31597 Mdot .70317 .31752 Mdot .70952 .30006 Mdot .71587 .31557 Mdot .72222 .32239 Mdot .72857 .31204 Mdot .73492 .30535 Mdot .74127 .30889 Mdot .74762 .31505 Mdot .75397 .3039 Mdot .76032 .30613 Mdot .76667 .31524 Mdot .77302 .31766 Mdot .77937 .30245 Mdot .78571 .31356 Mdot .79206 .31875 Mdot .79841 .32176 Mdot .80476 .30273 Mdot .81111 .30603 Mdot .81746 .31307 Mdot .82381 .30701 Mdot .83016 .30888 Mdot .83651 .30361 Mdot .84286 .31412 Mdot .84921 .30018 Mdot .85556 .30151 Mdot .8619 .32496 Mdot .86825 .32536 Mdot .8746 .31635 Mdot .88095 .3161 Mdot .8873 .31062 Mdot .89365 .31321 Mdot .9 .31073 Mdot .90635 .30949 Mdot .9127 .31427 Mdot .91905 .30708 Mdot .9254 .30277 Mdot .93175 .30716 Mdot .9381 .31158 Mdot .94444 .30394 Mdot .95079 .30811 Mdot .95714 .31015 Mdot .96349 .31241 Mdot .96984 .30907 Mdot .97619 .30902 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooo00<0003oooooool00_ooo`040000oooooooo00001?ooo`030000oooooooo 0?ooool3oooo000>oooo0`0000?oool200001Oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool00`000?ooooooo`03oooo00<0 003oooooool0o?ooo`006oooo`030000oooooooo00?oool00`000?ooooooo`3loooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?oo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool01Oooo`030000oooooooo 0?[oool001_oool00`000?ooooooo`05oooo00<0003oooooool0n_ooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?ooo`006ooo o`030000oooooooo00[oool00`000?ooooooo`3eoooo000Koooo00<0003oooooool02_ooo`030000 oooooooo0?Goool000Ooool500000_ooo`800004oooo0P0000Goool00`000?ooooooo`06oooo00<0 003oooooool0nOooo`002Oooo`050000oooooooooooo000000;oool010000?ooooooo`0000;oool0 0`000?ooooooo`02oooo00<0003oooooool01_ooo`030000oooooooo0?Woool000Woool01@000?oo ooooooooo`000002oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`<0003ooooo0ooo o`002Oooo`050000oooooooooooo000000;oool010000?ooooooo`0000;oool00`000?ooooooo`02 oooo00<0003oooooool0ooooo`?oool000Woool01@000?ooooooooooo`000002oooo00@0003ooooo ool00002oooo00<0003oooooool00_ooo`030000oooooooo0?ooool3oooo0008oooo0P0000Coool2 00001?ooo`800005oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`030000oooooooo0?ooool3oooo000Koooo0P000?ooool4oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool02?ooo`030000oooooooo0?Ooool001_oool200002Oooo`030000 oooooooo0?Ooool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006ooo o`80003ooooo1?ooo`006oooo`030000oooooooo01Coool00`000?ooooooo`0aoooo00<0003ooooo ool0]oooo`006oooo`030000oooooooo00_oool00`000?ooooooo`06oooo00<0003oooooool0oooo0P0000Woool00`000?oo ooooo`0:oooo00D0003oooooooooool000001?ooo`030000oooooooo00[oool2000000Coool0003o ool0000=oooo00@0003oool0003oool200000oooo`060000oooooooo0000oooo00000_ooo`050000 oooo00000000oooo0080000>oooo0009oooo00<0003oooooool00_ooo`800003oooo00@0003ooooo ool00004oooo00<0003oooooool0COooo`030000oooooooo00Ooool00`000?ooooooo`05oooo00<0 003oooooool01_ooo`040000oooooooo00000_ooo`030000oooo000001?oool02@000?oooooooooo o`000?ooo`000?ooo`00000:oooo00@0003oooooooooool200002Oooo`030000oooo000000;oool0 0`000?ooooooo`02oooo00@0003oooooool00004oooo00<0003oooooool00_ooo`030000oooooooo 00;oool00`000?ooooooo`05oooo00<0003oooooool01?ooo`030000oooooooo00Goool01`000?oo o`0000000?ooo`000?ooo`02000000?oool0003oool01Oooo`030000oooooooo00;oool200004Ooo o`002Oooo`030000oooooooo00;oool00`000?ooooooo`02oooo00@0003oooooool00004oooo00<0 003oooooool0@_ooo`030000oooooooo00Soool00`000?ooooooo`07oooo00<0003oooooool01Ooo o`030000oooooooo00Koool00`000?ooooooo`03oooo00@0003oool00000000Boooo00D0003ooooo ooooool000003_ooo`030000oooooooo00Coool00`000?ooooooo`07oooo00H0003oooooool0003o ool00002oooo00<0003oooooool01Oooo`030000oooooooo00;oool00`000?ooo`000002oooo00<0 003oool000003?ooo`030000oooooooo00Goool00`000?ooo`000007oooo00<0003oooooool07?oo o`002?ooo`800004oooo0`0000?oool200001Oooo`030000oooooooo04;oool00`000?ooooooo`0I oooo00@0003oooooool0000?oooo00<0003oool000003?ooo`030000oooooooo01_oool00`000?oo ooooo`03oooo00<0003oooooool01_ooo`030000oooooooo00;oool00`000?ooooooo`0:oooo00<0 003oooooool00_ooo`80000loooo000Koooo00<0003oooooool0oooo00<0 003oooooool0Goooo`006oooo`030000oooooooo01coool00`000?ooooooo`0oooo`030000oooooooo0?ooo`030000oooooooo0"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -22.9235, \ 0.607629, 1.8727}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 1.73472e-017 0.00618034 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .12361 -12 -4.5 ] [.01131 .12361 0 4.5 ] [.01131 .24721 -12 -4.5 ] [.01131 .24721 0 4.5 ] [.01131 .37082 -12 -4.5 ] [.01131 .37082 0 4.5 ] [.01131 .49443 -12 -4.5 ] [.01131 .49443 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .12361 m .03006 .12361 L s [(20)] .01131 .12361 1 0 Mshowa .02381 .24721 m .03006 .24721 L s [(40)] .01131 .24721 1 0 Mshowa .02381 .37082 m .03006 .37082 L s [(60)] .01131 .37082 1 0 Mshowa .02381 .49443 m .03006 .49443 L s [(80)] .01131 .49443 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(100)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0309 m .02756 .0309 L s .02381 .0618 m .02756 .0618 L s .02381 .09271 m .02756 .09271 L s .02381 .15451 m .02756 .15451 L s .02381 .18541 m .02756 .18541 L s .02381 .21631 m .02756 .21631 L s .02381 .27812 m .02756 .27812 L s .02381 .30902 m .02756 .30902 L s .02381 .33992 m .02756 .33992 L s .02381 .40172 m .02756 .40172 L s .02381 .43262 m .02756 .43262 L s .02381 .46353 m .02756 .46353 L s .02381 .52533 m .02756 .52533 L s .02381 .55623 m .02756 .55623 L s .02381 .58713 m .02756 .58713 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 .59331 Mdot .03651 .55623 Mdot .04286 .50679 Mdot .04921 .3461 Mdot .05556 .25751 Mdot .0619 .30902 Mdot .06825 .33992 Mdot .0746 .36258 Mdot .08095 .39554 Mdot .0873 .19571 Mdot .09365 .3976 Mdot .1 .53893 Mdot .10635 .39637 Mdot .1127 .4388 Mdot .11905 .30593 Mdot .1254 .41532 Mdot .13175 .10801 Mdot .1381 .26982 Mdot .14444 .26905 Mdot .15079 .14597 Mdot .15714 .14307 Mdot .16349 .13942 Mdot .16984 .22988 Mdot .17619 .14021 Mdot .18254 .13047 Mdot .18889 .20051 Mdot .19524 .19795 Mdot .20159 .2571 Mdot .20794 .19146 Mdot .21429 .1161 Mdot .22063 .17319 Mdot .22698 .16214 Mdot .23333 .14777 Mdot .23968 .52542 Mdot .24603 .30696 Mdot .25238 .16298 Mdot .25873 .10891 Mdot .26508 .20124 Mdot .27143 .28905 Mdot .27778 .18306 Mdot .28413 .30704 Mdot .29048 .12835 Mdot .29683 .17885 Mdot .30317 .16263 Mdot .30952 .14143 Mdot .31587 .114 Mdot .32222 .14798 Mdot .32857 .13902 Mdot .33492 .15224 Mdot .34127 .0808 Mdot .34762 .10354 Mdot .35397 .13016 Mdot .36032 .2092 Mdot .36667 .11208 Mdot .37302 .18722 Mdot .37937 .16213 Mdot .38571 .08667 Mdot .39206 .12034 Mdot .39841 .09999 Mdot .40476 .09903 Mdot .41111 .19928 Mdot .41746 .18907 Mdot .42381 .12097 Mdot .43016 .1709 Mdot .43651 .06732 Mdot .44286 .09431 Mdot .44921 .07575 Mdot .45556 .09763 Mdot .4619 .06071 Mdot .46825 .09263 Mdot .4746 .09017 Mdot .48095 .06898 Mdot .4873 .11186 Mdot .49365 .08896 Mdot .5 .09637 Mdot .50635 .06668 Mdot .5127 .06076 Mdot .51905 .08965 Mdot .5254 .09944 Mdot .53175 .09746 Mdot .5381 .0523 Mdot .54444 .06921 Mdot .55079 .08317 Mdot .55714 .04724 Mdot .56349 .06971 Mdot .56984 .0819 Mdot .57619 .08496 Mdot .58254 .04539 Mdot .58889 .08592 Mdot .59524 .04452 Mdot .60159 .11343 Mdot .60794 .06137 Mdot .61429 .04835 Mdot .62063 .06353 Mdot .62698 .0527 Mdot .63333 .05013 Mdot .63968 .05164 Mdot .64603 .06126 Mdot .65238 .0418 Mdot .65873 .05485 Mdot .66508 .05536 Mdot .67143 .0561 Mdot .67778 .05352 Mdot .68413 .07046 Mdot .69048 .05625 Mdot .69683 .04188 Mdot .70317 .06158 Mdot .70952 .07359 Mdot .71587 .05011 Mdot .72222 .05451 Mdot .72857 .07302 Mdot .73492 .0462 Mdot .74127 .07448 Mdot .74762 .03736 Mdot .75397 .03827 Mdot .76032 .04014 Mdot .76667 .04624 Mdot .77302 .04132 Mdot .77937 .06626 Mdot .78571 .02917 Mdot .79206 .02502 Mdot .79841 .03661 Mdot .80476 .03379 Mdot .81111 .05174 Mdot .81746 .02187 Mdot .82381 .04861 Mdot .83016 .0423 Mdot .83651 .02458 Mdot .84286 .01611 Mdot .84921 .0341 Mdot .85556 .04219 Mdot .8619 .03502 Mdot .86825 .02763 Mdot .8746 .03552 Mdot .88095 .03104 Mdot .8873 .02513 Mdot .89365 .01811 Mdot .9 .01952 Mdot .90635 .02699 Mdot .9127 .0197 Mdot .91905 .01965 Mdot .9254 .02169 Mdot .93175 .0115 Mdot .9381 .01607 Mdot .94444 .01944 Mdot .95079 .01137 Mdot .95714 .00968 Mdot .96349 .01051 Mdot .96984 .00412 Mdot .97619 0 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgSoool00`000?ooooooo`02oooo00@0 003oool00000000Aoooo000Koooo00<0003oooooool0dOooo`030000oooooooo01Coool00`000?oo o`000002oooo00@0003oool00000000Aoooo000Koooo00<0003oooooool0dOooo`030000oooooooo 00[oool00`000?ooo`000002oooo00<0003oool000001?ooo`80000Foooo000Koooo00<0003ooooo ool0b_ooo`030000oooooooo017oool00`000?ooo`000002oooo00@0003oool000000004oooo00<0 003oooooool05?ooo`006oooo`030000oooooooo0 oooo00<0003oooooool09_ooo`030000oooooooo03ooool001_oool00`000?ooooooo`1Xoooo00<0 003oooooool02?ooo`030000oooooooo00Coool00`000?ooooooo`07oooo00D0003oooooooooool0 00007oooo`030000oooooooo00?oool00`000?ooooooo`02oooo00<0003oooooool0C?ooo`006ooo o`030000oooooooo06_oool00`000?ooooooo`0joooo00<0003oooooool00oooo`030000oooooooo 00;oool01@000?ooooooooooo`00001:oooo000Koooo00<0003oooooool0Coooo`030000oooooooo 01Woool00`000?ooooooo`19oooo00<0003oooooool0B?ooo`006oooo`030000oooooooo04ooool0 0`000?ooooooo`0coooo00<0003oooooool00_ooo`030000oooo000007Goool001_oool00`000?oo ooooo`1Joooo00<0003oooooool06Oooo`030000oooooooo00coool00`000?ooooooo`02oooo00<0 003oool000000_ooo`030000oooooooo073oool001_oool00`000?ooooooo`1Joooo00<0003ooooo ool04oooo`800004oooo00<0003oooooool01?ooo`030000oooooooo00ooool00`000?ooooooo`1` oooo000Koooo0P0006[oool00`000?ooooooo`04oooo0P0000Koool00`000?ooooooo`02oooo00<0 003oooooool0P_ooo`006oooo`030000oooooooo05koool200002Oooo`050000oooooooooooo0000 00[oool00`000?ooooooo`04oooo0P00087oool001_oool00`000?ooooooo`1Aoooo00<0003ooooo ool02_ooo`80000=oooo00<0003oooooool03oooo`800021oooo000Koooo00<0003oooooool06Ooo o`030000oooooooo03Goool00`000?ooooooo`2^oooo000Koooo00<0003oooooool06Oooo`030000 oooooooo01goool00`000?ooooooo`0Ioooo00<0003oooooool07Oooo`030000oooooooo08[oool0 01_oool00`000?ooooooo`0^oooo00<0003oooooool02?ooo`030000oooooooo00coool00`000?oo ooooo`0:oooo00<0003oooooool07Oooo`030000oooooooo01[oool00`000?ooooooo`1]oooo000= oooo100000?oool200001Oooo`030000oooooooo02koool00`000?ooooooo`0Goooo00<0003ooooo ool04Oooo`030000oooooooo03?oool00`000?ooooooo`1]oooo000=oooo00<0003oooooool00ooo o`040000oooooooo00001?ooo`030000oooooooo05coool00`000?ooooooo`05oooo00<0003ooooo ool0Voooo`003_ooo`030000oooooooo00;oool010000?ooooooo`0000Coool30000I?ooo`030000 oooooooo09_oool000ooool01@000?ooooooooooo`000002oooo00<0003oooooool00_ooo`030000 oooooooo02Koool00`000?ooooooo`0Ioooo00<0003oooooool03Oooo`030000oooooooo0:goool0 00goool010000?ooooooo`0000;oool010000?ooooooo`0000Coool00`000?ooooooo`0Voooo00<0 003oooooool06Oooo`030000oooooooo00goool00`000?ooooooo`2]oooo000>oooo0P0000Coool2 00001Oooo`030000oooooooo027oool00`000?ooooooo`0Xoooo00<0003oooooool0/oooo`006ooo o`030000oooooooo01ooool00`000?ooo`000002oooo00<0003oooooool08?ooo`030000oooooooo 00;oool00`000?ooooooo`2coooo000Koooo00<0003oooooool07_ooo`800004oooo00<0003ooooo ool08?ooo`030000oooooooo0;Soool001_oool00`000?ooooooo`0Noooo00<0003oooooool04_oo o`030000oooooooo01Coool00`000?ooooooo`2eoooo000Koooo00<0003oooooool0Goool0 01_oool00`000?ooooooo`0Joooo00<0003oool00000iOooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo0P000?ooool4oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`0moooo00<0003oooooool0`_ooo`006oooo`030000oooooooo03goool00`000?ooooooo`32 oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool01_ooo`030000oooooooo00coool0 0`000?ooooooo`0Noooo00<0003oooooool01oooo`030000oooooooo0;ooool001_oool200001ooo o`030000oooooooo00coool00`000?ooooooo`0Noooo00<0003oooooool01oooo`030000oooooooo 0;ooool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`08 oooo00<0003oooooool0moooo`006oooo`800009oooo00<0003oooooool0moooo`006oooo`030000 oooooooo00?oool00`000?ooooooo`3loooo000Koooo00<0003oooooool00oooo`030000oooooooo 0?coool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000K oooo00<0003oooooool02_ooo`030000oooooooo0?Goool000goool300001?ooo`800005oooo00<0 003oooooool02_ooo`030000oooooooo0?Goool000goool010000?ooooooo`0000;oool010000?oo ooooo`0000Coool00`000?ooooooo`3ooooo0oooo`003Oooo`040000oooooooo00000_ooo`040000 oooooooo00001?ooo`<0003ooooo0oooo`003Oooo`<00003oooo00@0003oooooool00004oooo00<0 003oooooool0ooooo`?oool000koool00`000?ooooooo`02oooo00@0003oooooool00004oooo00<0 003oooooool0ooooo`?oool000koool300000oooo`800005oooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool02oooo`050000oooooooooooo000000;oool00`000?ooooooo`3]oooo000Koooo00<0 003oooooool02oooo`050000oooooooooooo000000;oool00`000?ooooooo`3]oooo000Koooo0P00 0?ooool4oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`030000oooooooo01Ooool00`000?ooooooo`3Xoooo000Koooo00<0003oooooool05ooo o`030000oooooooo0>Soool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool0 0`000?ooooooo`0Doooo00<0003oooooool0joooo`006oooo`030000oooooooo01Coool00`000?oo ooooo`3[oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?ooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool000koool200001?oo o`800005oooo00<0003oooooool0ooooo`?oool000goool010000?ooooooo`0000;oool010000?oo ooooo`0000Coool00`000?ooooooo`3ooooo0oooo`003Oooo`040000oooooooo00000_ooo`040000 oooooooo00001?ooo`<0003ooooo0oooo`003_ooo`800003oooo00@0003oooooool00004oooo00<0 003oooooool0ooooo`?oool000goool010000?ooooooo`0000;oool010000?ooooooo`0000Coool0 0`000?ooooooo`3ooooo0oooo`003_ooo`800004oooo0P0000Goool00`000?ooooooo`02oooo00<0 003oooooool0oOooo`006oooo`030000oooooooo00;oool00`000?ooooooo`3moooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 03Goool00`000?ooooooo`3:oooo000Koooo0P0003Koool00`000?ooooooo`3:oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 013oool00`000?ooooooo`3_oooo000Koooo00<0003oooooool04?ooo`030000oooooooo0>ooool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00@0 003oooooool0003ooooo0_ooo`006oooo`8000000oooo`000?ooo`3ooooo0Oooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3o oooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo0P00 0?ooool4oooo000Koooo0P000?ooool4oooo000Koooo0P000?ooool4oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo0007oooo1@0000;oool200001?ooo`800005oooo00<0003oooooool0ooooo`?oool000Woool0 1@000?ooooooooooo`000002oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`030000 oooooooo0?ooool3oooo0009oooo00D0003oooooooooool000000_ooo`040000oooooooo00000_oo o`030000oooooooo00;oool30000ooooo`?oool000Woool01@000?ooooooooooo`000002oooo00@0 003oooooool00002oooo00<0003oooooool0ooooo`Soool000Woool01@000?ooooooooooo`000002 oooo00@0003oooooool00002oooo00<0003oooooool0ooooo`Soool000Soool200001?ooo`800004 oooo0P000?ooool;oooo003ooooo8Oooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -7.64114, \ 0.607629, 0.624232}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 -2.60209e-017 0.00206011 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .10301 -12 -4.5 ] [.01131 .10301 0 4.5 ] [.01131 .20601 -18 -4.5 ] [.01131 .20601 0 4.5 ] [.01131 .30902 -18 -4.5 ] [.01131 .30902 0 4.5 ] [.01131 .41202 -18 -4.5 ] [.01131 .41202 0 4.5 ] [.01131 .51503 -18 -4.5 ] [.01131 .51503 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .10301 m .03006 .10301 L s [(50)] .01131 .10301 1 0 Mshowa .02381 .20601 m .03006 .20601 L s [(100)] .01131 .20601 1 0 Mshowa .02381 .30902 m .03006 .30902 L s [(150)] .01131 .30902 1 0 Mshowa .02381 .41202 m .03006 .41202 L s [(200)] .01131 .41202 1 0 Mshowa .02381 .51503 m .03006 .51503 L s [(250)] .01131 .51503 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(300)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0206 m .02756 .0206 L s .02381 .0412 m .02756 .0412 L s .02381 .0618 m .02756 .0618 L s .02381 .0824 m .02756 .0824 L s .02381 .12361 m .02756 .12361 L s .02381 .14421 m .02756 .14421 L s .02381 .16481 m .02756 .16481 L s .02381 .18541 m .02756 .18541 L s .02381 .22661 m .02756 .22661 L s .02381 .24721 m .02756 .24721 L s .02381 .26781 m .02756 .26781 L s .02381 .28842 m .02756 .28842 L s .02381 .32962 m .02756 .32962 L s .02381 .35022 m .02756 .35022 L s .02381 .37082 m .02756 .37082 L s .02381 .39142 m .02756 .39142 L s .02381 .43262 m .02756 .43262 L s .02381 .45322 m .02756 .45322 L s .02381 .47383 m .02756 .47383 L s .02381 .49443 m .02756 .49443 L s .02381 .53563 m .02756 .53563 L s .02381 .55623 m .02756 .55623 L s .02381 .57683 m .02756 .57683 L s .02381 .59743 m .02756 .59743 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 .00618 Mdot .03651 .0309 Mdot .04286 .05562 Mdot .04921 .13185 Mdot .05556 .15451 Mdot .0619 .19777 Mdot .06825 .24515 Mdot .0746 .19365 Mdot .08095 .27812 Mdot .0873 .28533 Mdot .09365 .41017 Mdot .1 .33621 Mdot .10635 .50215 Mdot .1127 .274 Mdot .11905 .42335 Mdot .1254 .32962 Mdot .13175 .48155 Mdot .1381 .3589 Mdot .14444 .34473 Mdot .15079 .38848 Mdot .15714 .28121 Mdot .16349 .29686 Mdot .16984 .40038 Mdot .17619 .4969 Mdot .18254 .29099 Mdot .18889 .33496 Mdot .19524 .33738 Mdot .20159 .34631 Mdot .20794 .34893 Mdot .21429 .45646 Mdot .22063 .32669 Mdot .22698 .38142 Mdot .23333 .37496 Mdot .23968 .32695 Mdot .24603 .38061 Mdot .25238 .54176 Mdot .25873 .34411 Mdot .26508 .40904 Mdot .27143 .35993 Mdot .27778 .34698 Mdot .28413 .36923 Mdot .29048 .32058 Mdot .29683 .30255 Mdot .30317 .32795 Mdot .30952 .3717 Mdot .31587 .27458 Mdot .32222 .34178 Mdot .32857 .3526 Mdot .33492 .31474 Mdot .34127 .34082 Mdot .34762 .35847 Mdot .35397 .33274 Mdot .36032 .3311 Mdot .36667 .35 Mdot .37302 .31491 Mdot .37937 .28055 Mdot .38571 .33985 Mdot .39206 .33444 Mdot .39841 .32244 Mdot .40476 .31552 Mdot .41111 .32184 Mdot .41746 .34497 Mdot .42381 .32647 Mdot .43016 .3039 Mdot .43651 .31471 Mdot .44286 .34456 Mdot .44921 .31297 Mdot .45556 .33854 Mdot .4619 .31626 Mdot .46825 .31659 Mdot .4746 .31874 Mdot .48095 .32306 Mdot .4873 .28725 Mdot .49365 .35273 Mdot .5 .30312 Mdot .50635 .30783 Mdot .5127 .29676 Mdot .51905 .32933 Mdot .5254 .36197 Mdot .53175 .32134 Mdot .5381 .29731 Mdot .54444 .31659 Mdot .55079 .32757 Mdot .55714 .28458 Mdot .56349 .31709 Mdot .56984 .31298 Mdot .57619 .31267 Mdot .58254 .29314 Mdot .58889 .34328 Mdot .59524 .2979 Mdot .60159 .32746 Mdot .60794 .32739 Mdot .61429 .29969 Mdot .62063 .31704 Mdot .62698 .32614 Mdot .63333 .31242 Mdot .63968 .31016 Mdot .64603 .3177 Mdot .65238 .34233 Mdot .65873 .30513 Mdot .66508 .32571 Mdot .67143 .32332 Mdot .67778 .31181 Mdot .68413 .31412 Mdot .69048 .33437 Mdot .69683 .31597 Mdot .70317 .31752 Mdot .70952 .30006 Mdot .71587 .31557 Mdot .72222 .32239 Mdot .72857 .31204 Mdot .73492 .30535 Mdot .74127 .30889 Mdot .74762 .31505 Mdot .75397 .3039 Mdot .76032 .30613 Mdot .76667 .31524 Mdot .77302 .31766 Mdot .77937 .30245 Mdot .78571 .31356 Mdot .79206 .31875 Mdot .79841 .32176 Mdot .80476 .30273 Mdot .81111 .30603 Mdot .81746 .31307 Mdot .82381 .30701 Mdot .83016 .30888 Mdot .83651 .30361 Mdot .84286 .31412 Mdot .84921 .30018 Mdot .85556 .30151 Mdot .8619 .32496 Mdot .86825 .32536 Mdot .8746 .31635 Mdot .88095 .3161 Mdot .8873 .31062 Mdot .89365 .31321 Mdot .9 .31073 Mdot .90635 .30949 Mdot .9127 .31427 Mdot .91905 .30708 Mdot .9254 .30277 Mdot .93175 .30716 Mdot .9381 .31158 Mdot .94444 .30394 Mdot .95079 .30811 Mdot .95714 .31015 Mdot .96349 .31241 Mdot .96984 .30907 Mdot .97619 .30902 Mdot .5 Mabswid .02381 .37082 m .06244 .37082 L .10458 .37082 L .14415 .37082 L .18221 .37082 L .22272 .37082 L .26171 .37082 L .30316 .37082 L .34309 .37082 L .3815 .37082 L .42237 .37082 L .46172 .37082 L .49955 .37082 L .53984 .37082 L .57861 .37082 L .61984 .37082 L .65954 .37082 L .69774 .37082 L .73838 .37082 L .77751 .37082 L .81909 .37082 L .85916 .37082 L .89771 .37082 L .93871 .37082 L .97619 .37082 L s .02381 .24721 m .06244 .24721 L .10458 .24721 L .14415 .24721 L .18221 .24721 L .22272 .24721 L .26171 .24721 L .30316 .24721 L .34309 .24721 L .3815 .24721 L .42237 .24721 L .46172 .24721 L .49955 .24721 L .53984 .24721 L .57861 .24721 L .61984 .24721 L .65954 .24721 L .69774 .24721 L .73838 .24721 L .77751 .24721 L .81909 .24721 L .85916 .24721 L .89771 .24721 L .93871 .24721 L .97619 .24721 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooo00<0003oooooool00_ooo`040000oooooooo00001?ooo`030000oooooooo 0?ooool3oooo000>oooo0`0000?oool200001Oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool00`000?ooooooo`03oooo00<0 003oooooool0o?ooo`006oooo`030000oooooooo00?oool00`000?ooooooo`3loooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?oo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool01Oooo`030000oooooooo 0?[oool001_oool00`000?ooooooo`05oooo00<0003oooooool0n_ooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?ooo`006ooo o`030000oooooooo00[oool00`000?ooooooo`3eoooo000Koooo00<0003oooooool02_ooo`030000 oooooooo0?Goool000Ooool500000_ooo`800004oooo0P0000Goool00`000?ooooooo`06oooo00<0 003oooooool0nOooo`002Oooo`050000oooooooooooo000000;oool010000?ooooooo`0000;oool0 0`000?ooooooo`02oooo00<0003oooooool01_ooo`030000oooooooo0?Woool000Woool01@000?oo ooooooooo`000002oooo00@0003oooooool00002oooo00<0003oooooool00_ooo`<0003ooooo0ooo o`002Oooo`050000oooooooooooo000000;oool010000?ooooooo`0000;oool00`000?ooooooo`02 oooo00<0003oooooool0ooooo`?oool000Woool01@000?ooooooooooo`000002oooo00@0003ooooo ool00002oooo00<0003oooooool00_ooo`030000oooooooo0?ooool3oooo0008oooo0P0000Coool2 00001?ooo`800005oooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`030000oooooooo0?ooool3oooo000Koooo0P000?ooool4oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo00<0003oooooool02?ooo`030000oooooooo0?Ooool001_ooooh00003Oooo`006ooo o`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo0P000?ooool4oooo000K oooo00<0003oooooool05?ooo`030000oooooooo037oool00`000?ooooooo`2goooo000Koooo00<0 003oooooool02oooo`030000oooooooo00Koool00`000?ooooooo`0aoooo00<0003oooooool0]ooo o`006oooo`030000oooooooo00_oool00`000?ooooooo`0Aoooo00<0003oooooool0=oooo`030000 oooooooo0:Koool001_oool00`000?ooooooo`0=oooo00<0003oooooool03oooo`030000oooooooo 03Ooool00`000?ooooooo`0[oooo00<0003oooooool0N?ooo`006oooo`030000oooooooo00goool0 0`000?ooooooo`1Uoooo00<0003oooooool03oooo`030000oooooooo07Soool001_oool200009ooo o`030000oooooooo04coool00`000?ooooooo`0Eoooo00<0003oooooool0L_ooo`006oooo`030000 oooooooo027oool00`000?ooooooo`02oooo00<0003oooooool0D_ooo`030000oooooooo00Coool0 0`000?ooooooo`08oooo00<0003oooooool0L_ooo`006oooo`030000oooooooo027oool00`000?oo ooooo`1Goooo00<0003oooooool01?ooo`030000oooooooo00coool00`000?ooooooo`02oooo00<0 003oooooool05Oooo`030000oooooooo02;oool20000;Oooo`001oooo`D00002oooo0P0000Coool2 00001Oooo`030000oooooooo04?oool00`000?ooooooo`0Poooo00<0003oooooool03oooo`030000 oooooooo01Koool00`000?ooooooo`02oooo00<0003oooooool02?ooo`030000oooooooo00[oool0 0`000?ooooooo`04oooo00<0003oooooool00_ooo`030000oooooooo00?oool00`000?ooooooo`04 oooo00<0003oooooool01Oooo`040000oooooooooooo0P00017oool00`000?ooooooo`02oooo00<0 003oooooool05?ooo`002Oooo`050000oooooooooooo000000;oool010000?ooooooo`0000;oool0 0`000?ooooooo`02oooo00<0003oooooool0@oooo`030000oooooooo023oool00`000?ooooooo`0? oooo00<0003oool000009_ooo`030000oooooooo017oool00`000?ooo`000002oooo00<0003oool0 00000oooo`030000oooooooo00Coool00`000?ooo`000002oooo00@0003oool00000000Eoooo0P00 0007oooo0000oooooooo0000oooo000000Coool200003_ooo`002Oooo`030000oooooooo00Coool0 10000?ooooooo`0000;oool00`000?ooooooo`02oooo0`0006_oool00`000?ooooooo`0oooo00<0 003oooooool01?ooo`030000oooooooo00Ooool01P000?ooooooo`000?ooo`0000;oool00`000?oo ooooo`05oooo00<0003oooooool00_ooo`030000oooo000000;oool00`000?ooo`00000oooo00<0003oooooool00_ooo`030000oooooooo00Soool00`000?oo ooooo`0@oooo00<0003oooooool07oooo`030000oooooooo00koool00`000?ooooooo`1Ooooo000K oooo00<0003oooooool07?ooo`030000oooooooo00coool00`000?ooooooo`0;oooo00<0003ooooo ool00_ooo`030000oooooooo00Woool00`000?ooooooo`02oooo00<0003oooooool04Oooo`030000 oooooooo00?oool00`000?ooooooo`0Soooo00<0003oooooool03_ooo`030000oooooooo05ooool0 01_oool00`000?ooooooo`0Loooo00<0003oooooool03?ooo`80000Aoooo00<0003oooooool05?oo o`030000oooooooo00_oool00`000?ooooooo`03oooo00<0003oooooool0U_ooo`006oooo`80000] oooo00<0003oooooool07Oooo`030000oooooooo00Koool00`000?ooooooo`0Noooo00<0003ooooo ool0ROooo`006oooo`030000oooooooo01[oool00`000?ooooooo`0_oooo00<0003oooooool00_oo o`030000oooooooo02;oool00`000?ooooooo`29oooo000Koooo00<0003oooooool06_ooo`030000 oooooooo023oool00`000?ooooooo`0Aoooo00<0003oooooool0:oooo`030000oooooooo083oool0 01_oool00`000?ooooooo`0moooo00<0003oooooool0?oooo`030000oooooooo083oool001_oool0 0`000?ooooooo`10oooo00<0003oooooool0_oooo`006oooooP0000=oooo000Koooo00<0003ooooo ool07oool001_oool200007oooo`030000oooooooo0>7oool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`030000oooooooo02;oool00`000?ooooooo`3Moooo000Koooo00<0003oooooool08_oo o`030000oooooooo0=goool000Ooool400000oooo`800004oooo0P0000Goool00`000?ooooooo`0k oooo00<0003oooooool0a?ooo`001oooo`030000oooooooo00?oool010000?ooooooo`0000;oool0 10000?ooooooo`0000Coool00`000?ooooooo`0?oooo00<0003oooooool0:Oooo`030000oooooooo 0[oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003o oooo1?ooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo0P00 0?ooool4oooo000Koooo00<0003oooooool0;_ooo`030000oooooooo0=7oool001_oool00`000?oo ooooo`0^oooo00<0003oooooool0dOooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?oo o`006oooo`030000oooooooo01Woool00`000?ooooooo`3Voooo000Koooo00<0003oooooool06Ooo o`030000oooooooo0>Koool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo0P0002Goool00`000?ooooooo`3Koooo000Koooo00<0003oooooool04_oo o`030000oooooooo00ooool00`000?ooooooo`3Koooo000Koooo00<0003oooooool04_ooo`030000 oooooooo0>goool000Ooool400000oooo`800004oooo0P0000Goool00`000?ooooooo`3ooooo0ooo o`001oooo`030000oooooooo00?oool010000?ooooooo`0000;oool010000?ooooooo`0000Coool0 0`000?ooooooo`3ooooo0oooo`002?ooo`030000oooooooo00Goool010000?ooooooo`0000;oool0 0`000?ooooooo`02oooo0`000?ooool3oooo0009oooo00<0003oooooool00_ooo`800003oooo00@0 003oooooool00004oooo00<0003oooooool0ooooo`?oool000Ooool010000?ooooooo`0000?oool0 0`000?ooooooo`02oooo00@0003oooooool00004oooo00<0003oooooool0ooooo`?oool000Soool2 00001?ooo`<00003oooo0P0000Goool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool0 0`000?ooooooo`0hoooo00<0003oooooool0aoooo`006oooo`030000oooooooo03Soool00`000?oo ooooo`37oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`80003ooooo1?ooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo0P000?ooool4oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0oooo o`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?ooo`006oooo`030000 oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool000Soool200001?ooo`800004 oooo0P0000Goool00`000?ooooooo`3ooooo0oooo`001oooo`040000oooooooo00000_ooo`040000 oooooooo00000_ooo`040000oooooooo00001?ooo`030000oooooooo0?ooool3oooo0009oooo00D0 003oooooooooool000000_ooo`040000oooooooo00000_ooo`030000oooooooo00;oool30000oooo o`?oool000[oool010000?ooooooo`0000;oool010000?ooooooo`0000;oool00`000?ooooooo`3o oooo2?ooo`001oooo`040000oooooooo00000_ooo`040000oooooooo00000_ooo`040000oooooooo 0000ooooo`[oool000Soool200001?ooo`800004oooo0P000?ooool;oooo003ooooo8Oooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -22.9235, \ 0.607629, 1.8727}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.00634921 1.73472e-017 0.00618034 [ [.15079 -0.0125 -6 -9 ] [.15079 -0.0125 6 0 ] [.27778 -0.0125 -6 -9 ] [.27778 -0.0125 6 0 ] [.40476 -0.0125 -6 -9 ] [.40476 -0.0125 6 0 ] [.53175 -0.0125 -6 -9 ] [.53175 -0.0125 6 0 ] [.65873 -0.0125 -9 -9 ] [.65873 -0.0125 9 0 ] [.78571 -0.0125 -9 -9 ] [.78571 -0.0125 9 0 ] [.9127 -0.0125 -9 -9 ] [.9127 -0.0125 9 0 ] [.01131 .12361 -12 -4.5 ] [.01131 .12361 0 4.5 ] [.01131 .24721 -12 -4.5 ] [.01131 .24721 0 4.5 ] [.01131 .37082 -12 -4.5 ] [.01131 .37082 0 4.5 ] [.01131 .49443 -12 -4.5 ] [.01131 .49443 0 4.5 ] [.01131 .61803 -18 -4.5 ] [.01131 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15079 0 m .15079 .00625 L s [(20)] .15079 -0.0125 0 1 Mshowa .27778 0 m .27778 .00625 L s [(40)] .27778 -0.0125 0 1 Mshowa .40476 0 m .40476 .00625 L s [(60)] .40476 -0.0125 0 1 Mshowa .53175 0 m .53175 .00625 L s [(80)] .53175 -0.0125 0 1 Mshowa .65873 0 m .65873 .00625 L s [(100)] .65873 -0.0125 0 1 Mshowa .78571 0 m .78571 .00625 L s [(120)] .78571 -0.0125 0 1 Mshowa .9127 0 m .9127 .00625 L s [(140)] .9127 -0.0125 0 1 Mshowa .125 Mabswid .05556 0 m .05556 .00375 L s .0873 0 m .0873 .00375 L s .11905 0 m .11905 .00375 L s .18254 0 m .18254 .00375 L s .21429 0 m .21429 .00375 L s .24603 0 m .24603 .00375 L s .30952 0 m .30952 .00375 L s .34127 0 m .34127 .00375 L s .37302 0 m .37302 .00375 L s .43651 0 m .43651 .00375 L s .46825 0 m .46825 .00375 L s .5 0 m .5 .00375 L s .56349 0 m .56349 .00375 L s .59524 0 m .59524 .00375 L s .62698 0 m .62698 .00375 L s .69048 0 m .69048 .00375 L s .72222 0 m .72222 .00375 L s .75397 0 m .75397 .00375 L s .81746 0 m .81746 .00375 L s .84921 0 m .84921 .00375 L s .88095 0 m .88095 .00375 L s .94444 0 m .94444 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s .02381 .12361 m .03006 .12361 L s [(20)] .01131 .12361 1 0 Mshowa .02381 .24721 m .03006 .24721 L s [(40)] .01131 .24721 1 0 Mshowa .02381 .37082 m .03006 .37082 L s [(60)] .01131 .37082 1 0 Mshowa .02381 .49443 m .03006 .49443 L s [(80)] .01131 .49443 1 0 Mshowa .02381 .61803 m .03006 .61803 L s [(100)] .01131 .61803 1 0 Mshowa .125 Mabswid .02381 .0309 m .02756 .0309 L s .02381 .0618 m .02756 .0618 L s .02381 .09271 m .02756 .09271 L s .02381 .15451 m .02756 .15451 L s .02381 .18541 m .02756 .18541 L s .02381 .21631 m .02756 .21631 L s .02381 .27812 m .02756 .27812 L s .02381 .30902 m .02756 .30902 L s .02381 .33992 m .02756 .33992 L s .02381 .40172 m .02756 .40172 L s .02381 .43262 m .02756 .43262 L s .02381 .46353 m .02756 .46353 L s .02381 .52533 m .02756 .52533 L s .02381 .55623 m .02756 .55623 L s .02381 .58713 m .02756 .58713 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .03016 .59331 Mdot .03651 .55623 Mdot .04286 .50679 Mdot .04921 .3461 Mdot .05556 .25751 Mdot .0619 .30902 Mdot .06825 .33992 Mdot .0746 .36258 Mdot .08095 .39554 Mdot .0873 .19571 Mdot .09365 .3976 Mdot .1 .53893 Mdot .10635 .39637 Mdot .1127 .4388 Mdot .11905 .30593 Mdot .1254 .41532 Mdot .13175 .10801 Mdot .1381 .26982 Mdot .14444 .26905 Mdot .15079 .14597 Mdot .15714 .14307 Mdot .16349 .13942 Mdot .16984 .22988 Mdot .17619 .14021 Mdot .18254 .13047 Mdot .18889 .20051 Mdot .19524 .19795 Mdot .20159 .2571 Mdot .20794 .19146 Mdot .21429 .1161 Mdot .22063 .17319 Mdot .22698 .16214 Mdot .23333 .14777 Mdot .23968 .52542 Mdot .24603 .30696 Mdot .25238 .16298 Mdot .25873 .10891 Mdot .26508 .20124 Mdot .27143 .28905 Mdot .27778 .18306 Mdot .28413 .30704 Mdot .29048 .12835 Mdot .29683 .17885 Mdot .30317 .16263 Mdot .30952 .14143 Mdot .31587 .114 Mdot .32222 .14798 Mdot .32857 .13902 Mdot .33492 .15224 Mdot .34127 .0808 Mdot .34762 .10354 Mdot .35397 .13016 Mdot .36032 .2092 Mdot .36667 .11208 Mdot .37302 .18722 Mdot .37937 .16213 Mdot .38571 .08667 Mdot .39206 .12034 Mdot .39841 .09999 Mdot .40476 .09903 Mdot .41111 .19928 Mdot .41746 .18907 Mdot .42381 .12097 Mdot .43016 .1709 Mdot .43651 .06732 Mdot .44286 .09431 Mdot .44921 .07575 Mdot .45556 .09763 Mdot .4619 .06071 Mdot .46825 .09263 Mdot .4746 .09017 Mdot .48095 .06898 Mdot .4873 .11186 Mdot .49365 .08896 Mdot .5 .09637 Mdot .50635 .06668 Mdot .5127 .06076 Mdot .51905 .08965 Mdot .5254 .09944 Mdot .53175 .09746 Mdot .5381 .0523 Mdot .54444 .06921 Mdot .55079 .08317 Mdot .55714 .04724 Mdot .56349 .06971 Mdot .56984 .0819 Mdot .57619 .08496 Mdot .58254 .04539 Mdot .58889 .08592 Mdot .59524 .04452 Mdot .60159 .11343 Mdot .60794 .06137 Mdot .61429 .04835 Mdot .62063 .06353 Mdot .62698 .0527 Mdot .63333 .05013 Mdot .63968 .05164 Mdot .64603 .06126 Mdot .65238 .0418 Mdot .65873 .05485 Mdot .66508 .05536 Mdot .67143 .0561 Mdot .67778 .05352 Mdot .68413 .07046 Mdot .69048 .05625 Mdot .69683 .04188 Mdot .70317 .06158 Mdot .70952 .07359 Mdot .71587 .05011 Mdot .72222 .05451 Mdot .72857 .07302 Mdot .73492 .0462 Mdot .74127 .07448 Mdot .74762 .03736 Mdot .75397 .03827 Mdot .76032 .04014 Mdot .76667 .04624 Mdot .77302 .04132 Mdot .77937 .06626 Mdot .78571 .02917 Mdot .79206 .02502 Mdot .79841 .03661 Mdot .80476 .03379 Mdot .81111 .05174 Mdot .81746 .02187 Mdot .82381 .04861 Mdot .83016 .0423 Mdot .83651 .02458 Mdot .84286 .01611 Mdot .84921 .0341 Mdot .85556 .04219 Mdot .8619 .03502 Mdot .86825 .02763 Mdot .8746 .03552 Mdot .88095 .03104 Mdot .8873 .02513 Mdot .89365 .01811 Mdot .9 .01952 Mdot .90635 .02699 Mdot .9127 .0197 Mdot .91905 .01965 Mdot .9254 .02169 Mdot .93175 .0115 Mdot .9381 .01607 Mdot .94444 .01944 Mdot .95079 .01137 Mdot .95714 .00968 Mdot .96349 .01051 Mdot .96984 .00412 Mdot .97619 0 Mdot .5 Mabswid .02381 .12361 m .06244 .12361 L .10458 .12361 L .14415 .12361 L .18221 .12361 L .22272 .12361 L .26171 .12361 L .30316 .12361 L .34309 .12361 L .3815 .12361 L .42237 .12361 L .46172 .12361 L .49955 .12361 L .53984 .12361 L .57861 .12361 L .61984 .12361 L .65954 .12361 L .69774 .12361 L .73838 .12361 L .77751 .12361 L .81909 .12361 L .85916 .12361 L .89771 .12361 L .93871 .12361 L .97619 .12361 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgSoool00`000?ooooooo`02oooo00@0 003oool00000000Aoooo000Koooo00<0003oooooool0dOooo`030000oooooooo01Coool00`000?oo o`000002oooo00@0003oool00000000Aoooo000Koooo00<0003oooooool0dOooo`030000oooooooo 00[oool00`000?ooo`000002oooo00<0003oool000001?ooo`80000Foooo000Koooo00<0003ooooo ool0b_ooo`030000oooooooo017oool00`000?ooo`000002oooo00@0003oool000000004oooo00<0 003oooooool05?ooo`006oooo`030000oooooooo0 oooo00<0003oooooool09_ooo`030000oooooooo03ooool001_oool00`000?ooooooo`1Xoooo00<0 003oooooool02?ooo`030000oooooooo00Coool00`000?ooooooo`07oooo00D0003oooooooooool0 00007oooo`030000oooooooo00?oool00`000?ooooooo`02oooo00<0003oooooool0C?ooo`006ooo o`030000oooooooo06_oool00`000?ooooooo`0joooo00<0003oooooool00oooo`030000oooooooo 00;oool01@000?ooooooooooo`00001:oooo000Koooo00<0003oooooool0Coooo`030000oooooooo 01Woool00`000?ooooooo`19oooo00<0003oooooool0B?ooo`006oooo`030000oooooooo04ooool0 0`000?ooooooo`0coooo00<0003oooooool00_ooo`030000oooo000007Goool001_oool00`000?oo ooooo`1Joooo00<0003oooooool06Oooo`030000oooooooo00coool00`000?ooooooo`02oooo00<0 003oool000000_ooo`030000oooooooo073oool001_oool00`000?ooooooo`1Joooo00<0003ooooo ool04oooo`800004oooo00<0003oooooool01?ooo`030000oooooooo00ooool00`000?ooooooo`1` oooo000Koooo0P0006[oool00`000?ooooooo`04oooo0P0000Koool00`000?ooooooo`02oooo00<0 003oooooool0P_ooo`006oooo`030000oooooooo05koool200002Oooo`050000oooooooooooo0000 00[oool00`000?ooooooo`04oooo0P00087oool001_oool00`000?ooooooo`1Aoooo00<0003ooooo ool02_ooo`80000=oooo00<0003oooooool03oooo`800021oooo000Koooo00<0003oooooool06Ooo o`030000oooooooo03Goool00`000?ooooooo`2^oooo000Koooo00<0003oooooool06Oooo`030000 oooooooo01goool00`000?ooooooo`0Ioooo00<0003oooooool07Oooo`030000oooooooo08[oool0 01_oool00`000?ooooooo`0^oooo00<0003oooooool02?ooo`030000oooooooo00coool00`000?oo ooooo`0:oooo00<0003oooooool07Oooo`030000oooooooo01[oool00`000?ooooooo`1]oooo000= oooo100000?oool200001Oooo`030000oooooooo02koool00`000?ooooooo`0Goooo00<0003ooooo ool04Oooo`030000oooooooo03?oool00`000?ooooooo`1]oooo000=oooo00<0003oooooool00ooo o`040000oooooooo00001?ooo`030000oooooooo05coool00`000?ooooooo`05oooo00<0003ooooo ool0Voooo`003_ooo`030000oooooooo00;oool010000?ooooooo`0000Cooooh00003Oooo`003ooo o`050000oooooooooooo000000;oool00`000?ooooooo`02oooo00<0003oooooool09_ooo`030000 oooooooo01Woool00`000?ooooooo`0=oooo00<0003oooooool0[Oooo`003Oooo`040000oooooooo 00000_ooo`040000oooooooo00001?ooo`030000oooooooo02Koool00`000?ooooooo`0Ioooo00<0 003oooooool03Oooo`030000oooooooo0:goool000koool200001?ooo`800005oooo00<0003ooooo ool08Oooo`030000oooooooo02Soool00`000?ooooooo`2coooo000Koooo00<0003oooooool07ooo o`030000oooo000000;oool00`000?ooooooo`0Poooo00<0003oooooool00_ooo`030000oooooooo 0;?oool001_oool00`000?ooooooo`0Noooo0P0000Coool00`000?ooooooo`0Poooo00<0003ooooo ool0^?ooo`006oooo`030000oooooooo01koool00`000?ooooooo`0Boooo00<0003oooooool05?oo o`030000oooooooo0;Goool001_oool00`000?ooooooo`0coooo00<0003oooooool05?ooo`040000 oooooooo0000]?ooo`006oooo`80001>oooo00<0003oooooool0/_ooo`006oooo`030000oooooooo 037oool00`000?ooooooo`0Aoooo00<0003oooooool04Oooo`030000oooooooo0:Koool001_oool0 0`000?ooooooo`0aoooo00<0003oooooool01?ooo`030000oooooooo00[oool00`000?ooooooo`0A oooo00<0003oooooool0Y_ooo`006oooo`030000oooooooo03Soool00`000?ooooooo`37oooo000K oooo00<0003oooooool0goool001_oool00`000?ooooooo`0;oooo00D0 003oooooooooool000000_ooo`030000oooooooo0>goool001_oool20000ooooo`Coool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool05oooo`030000oooooooo0>Soool001_oool00`000?ooooooo`0Goooo00<0003oooooool0j?oo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`80003ooooo1?ooo`006oooo`030000oooooooo01Coool0 0`000?ooooooo`3[oooo000Koooo00<0003oooooool05?ooo`030000oooooooo0>_oool001_oool0 0`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003ooooo ool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3 oooo000Koooo0P000?ooool4oooo000Koooo00<0003oooooool0ooooo`?oool001_oool00`000?oo ooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0oooo o`?oool001_oool00`000?ooooooo`3ooooo0oooo`003_ooo`800004oooo0P0000Goool00`000?oo ooooo`3ooooo0oooo`003Oooo`040000oooooooo00000_ooo`040000oooooooo00001?ooo`030000 oooooooo0?ooool3oooo000=oooo00@0003oooooool00002oooo00@0003oooooool00004oooo0`00 0?ooool3oooo000>oooo0P0000?oool010000?ooooooo`0000Coool00`000?ooooooo`3ooooo0ooo o`003Oooo`040000oooooooo00000_ooo`040000oooooooo00001?ooo`030000oooooooo0?ooool3 oooo000>oooo0P0000Coool200001Oooo`030000oooooooo00;oool00`000?ooooooo`3moooo000K oooo00<0003oooooool00_ooo`030000oooooooo0?goool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0=Oooo`030000oooooooo 0<[oool001_oool20000=_ooo`030000oooooooo0<[oool001_oool00`000?ooooooo`3ooooo0ooo o`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool04?ooo`030000oooooooo 0>ooool001_oool00`000?ooooooo`0@oooo00<0003oooooool0koooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool010000?ooooooo`000?ooool2 oooo000Koooo0P000003oooo0000oooo0?ooool1oooo000Koooo00<0003oooooool0ooooo`?oool0 01_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo0?ooool3oooo000Koooo00<0 003oooooool0ooooo`?oool001_oool00`000?ooooooo`3ooooo0oooo`006oooo`030000oooooooo 0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool001_oool20000ooooo`Coool001_oool2 0000ooooo`Coool001_oool20000ooooo`Coool001_oool00`000?ooooooo`3ooooo0oooo`006ooo o`030000oooooooo0?ooool3oooo000Koooo00<0003oooooool0ooooo`?oool000Ooool500000_oo o`800004oooo0P0000Goool00`000?ooooooo`3ooooo0oooo`002Oooo`050000oooooooooooo0000 00;oool010000?ooooooo`0000;oool00`000?ooooooo`02oooo00<0003oooooool0ooooo`?oool0 00Woool01@000?ooooooooooo`000002oooo00@0003oooooool00002oooo00<0003oooooool00_oo o`<0003ooooo0oooo`002Oooo`050000oooooooooooo000000;oool010000?ooooooo`0000;oool0 0`000?ooooooo`3ooooo2?ooo`002Oooo`050000oooooooooooo000000;oool010000?ooooooo`00 00;oool00`000?ooooooo`3ooooo2?ooo`002?ooo`800004oooo0P0000Coool20000ooooo`_oool0 0?oooolQoooo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-16.7728, -7.64114, \ 0.607629, 0.624232}}] }, Open ]] }, Open ]], Cell[TextData[StyleBox["\tNow what would you estimate is a good size second \ catch to guarantee 20 percent or less error? If you only caught 30 fish in \ the second catch (thus equal to the first catch), what error would you expect \ from your numerical guess? What do you get when you try a guess?", FontSize->14]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(GuessPop[PopSize, 30, 30]\)], "Input"], Cell[BoxData[ \({225.`, 150, 50.`}\)], "Output"] }, Open ]], Cell[TextData[StyleBox["\tSo, what do you think? Is capture and re-capture a \ good method of estimating population? Why or why not?", FontSize->14]], "Text"], Cell[TextData[StyleBox["This notebook created by Dr. Garrett R. Love for the \ Shodor Education Foundation. Copyright 2001", "SmallText"]], "Text", FontSize->14] }, FrontEndVersion->"4.1 for Microsoft Windows", ScreenRectangle->{{0, 800}, {0, 527}}, ScreenStyleEnvironment->"Working", WindowSize->{520, 500}, WindowMargins->{{27, Automatic}, {Automatic, 0}}, StyleDefinitions -> "Classroom.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1705, 50, 103, 4, 66, "Subtitle"], Cell[1811, 56, 1128, 19, 282, "Text"], Cell[2942, 77, 433, 14, 71, "Text"], Cell[3378, 93, 54, 1, 50, "Input"], Cell[3435, 96, 859, 28, 112, "Text"], Cell[CellGroupData[{ Cell[4319, 128, 64, 1, 50, "Input"], Cell[4386, 131, 79, 1, 49, "Output"] }, Open ]], Cell[4480, 135, 577, 17, 117, "Text"], Cell[CellGroupData[{ Cell[5082, 156, 137, 2, 70, "Input"], Cell[5222, 160, 338, 5, 106, "Output"] }, Open ]], Cell[5575, 168, 534, 18, 72, "Text"], Cell[CellGroupData[{ Cell[6134, 190, 52, 1, 50, "Input"], Cell[6189, 193, 44, 1, 49, "Output"] }, Open ]], Cell[6248, 197, 297, 8, 71, "Text"], Cell[6548, 207, 59, 1, 50, "Input"], Cell[6610, 210, 428, 13, 82, "Text"], Cell[CellGroupData[{ Cell[7063, 227, 73, 1, 50, "Input"], Cell[7139, 230, 329, 4, 106, "Output"] }, Open ]], Cell[7483, 237, 428, 15, 52, "Text"], Cell[CellGroupData[{ Cell[7936, 256, 90, 1, 50, "Input"], Cell[8029, 259, 329, 4, 106, "Output"] }, Open ]], Cell[8373, 266, 1930, 71, 187, "Text"], Cell[10306, 339, 396, 7, 150, "Input"], Cell[10705, 348, 273, 11, 31, "Text"], Cell[CellGroupData[{ Cell[11003, 363, 43, 1, 50, "Input"], Cell[11049, 366, 317, 4, 106, "Output"] }, Open ]], Cell[11381, 373, 262, 8, 51, "Text"], Cell[11646, 383, 61, 1, 50, "Input"], Cell[11710, 386, 772, 20, 175, "Text"], Cell[CellGroupData[{ Cell[12507, 410, 41, 1, 50, "Input"], Cell[12551, 413, 53, 1, 49, "Output"] }, Open ]], Cell[12619, 417, 325, 12, 51, "Text"], Cell[CellGroupData[{ Cell[12969, 433, 48, 1, 50, "Input"], Cell[13020, 436, 35, 1, 49, "Output"] }, Open ]], Cell[13070, 440, 191, 3, 50, "Text"], Cell[CellGroupData[{ Cell[13286, 447, 57, 1, 50, "Input"], Cell[13346, 450, 35, 1, 49, "Output"] }, Open ]], Cell[13396, 454, 450, 16, 84, "Text"], Cell[CellGroupData[{ Cell[13871, 474, 82, 1, 50, "Input"], Cell[13956, 477, 36, 1, 49, "Output"] }, Open ]], Cell[14007, 481, 239, 8, 51, "Text"], Cell[CellGroupData[{ Cell[14271, 493, 64, 1, 50, "Input"], Cell[14338, 496, 44, 1, 49, "Output"] }, Open ]], Cell[14397, 500, 361, 12, 52, "Text"], Cell[CellGroupData[{ Cell[14783, 516, 176, 4, 90, "Input"], Cell[14962, 522, 78, 1, 49, "Output"] }, Open ]], Cell[15055, 526, 1275, 32, 310, "Text"], Cell[16333, 560, 127, 2, 70, "Input"], Cell[16463, 564, 353, 12, 52, "Text"], Cell[CellGroupData[{ Cell[16841, 580, 52, 1, 50, "Input"], Cell[16896, 583, 36, 1, 49, "Output"] }, Open ]], Cell[16947, 587, 787, 28, 94, "Text"], Cell[17737, 617, 406, 8, 110, "Input"], Cell[CellGroupData[{ Cell[18168, 629, 44, 1, 50, "Input"], Cell[18215, 632, 305, 4, 106, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[18557, 641, 44, 1, 50, "Input"], Cell[18604, 644, 46, 1, 49, "Output"] }, Open ]], Cell[18665, 648, 468, 16, 85, "Text"], Cell[19136, 666, 1088, 18, 370, "Input"], Cell[CellGroupData[{ Cell[20249, 688, 44, 1, 50, "Input"], Cell[20296, 691, 182, 3, 68, "Output"] }, Open ]], Cell[20493, 697, 363, 12, 63, "Text"], Cell[CellGroupData[{ Cell[20881, 713, 83, 1, 50, "Input"], Cell[20967, 716, 35, 1, 49, "Output"] }, Open ]], Cell[21017, 720, 705, 19, 185, "Text"], Cell[CellGroupData[{ Cell[21747, 743, 89, 1, 50, "Input"], Cell[21839, 746, 39, 1, 49, "Output"] }, Open ]], Cell[21893, 750, 650, 17, 135, "Text"], Cell[CellGroupData[{ Cell[22568, 771, 265, 4, 130, "Input"], Cell[22836, 777, 39, 1, 49, "Output"] }, Open ]], Cell[22890, 781, 365, 12, 51, "Text"], Cell[CellGroupData[{ Cell[23280, 797, 86, 1, 50, "Input"], Cell[23369, 800, 52, 1, 49, "Output"] }, Open ]], Cell[23436, 804, 358, 5, 90, "Text"], Cell[23797, 811, 541, 13, 110, "Text"], Cell[CellGroupData[{ Cell[24363, 828, 1572, 29, 470, "Input"], Cell[25938, 859, 80, 1, 49, "Output"] }, Open ]], Cell[26033, 863, 912, 26, 184, "Text"], Cell[26948, 891, 1455, 27, 450, "Input"], Cell[28406, 920, 131, 2, 50, "Text"], Cell[CellGroupData[{ Cell[28562, 926, 52, 1, 50, "Input"], Cell[28617, 929, 64, 1, 49, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[28718, 935, 54, 1, 50, "Input"], Cell[28775, 938, 80, 1, 49, "Output"] }, Open ]], Cell[28870, 942, 578, 13, 131, "Text"], Cell[CellGroupData[{ Cell[29473, 959, 53, 1, 50, "Input"], Cell[29529, 962, 49, 1, 49, "Output"] }, Open ]], Cell[29593, 966, 218, 3, 50, "Text"], Cell[CellGroupData[{ Cell[29836, 973, 55, 1, 50, "Input"], Cell[29894, 976, 51, 1, 49, "Output"] }, Open ]], Cell[29960, 980, 730, 23, 112, "Text"], Cell[CellGroupData[{ Cell[30715, 1007, 53, 1, 50, "Input"], Cell[30771, 1010, 85, 1, 49, "Output"] }, Open ]], Cell[30871, 1014, 1280, 42, 155, "Text"], Cell[32154, 1058, 347, 5, 130, "Input"], Cell[32504, 1065, 820, 25, 111, "Text"], Cell[CellGroupData[{ Cell[33349, 1094, 114, 2, 50, "Input"], Cell[33466, 1098, 21889, 611, 186, 6367, 415, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[55392, 1714, 108, 2, 50, "Input"], Cell[55503, 1718, 20706, 569, 186, 5927, 382, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[76224, 2290, 409, 9, 91, "Text"], Cell[CellGroupData[{ Cell[76658, 2303, 319, 7, 90, "Input"], Cell[CellGroupData[{ Cell[77002, 2314, 15443, 456, 186, 4484, 316, "GraphicsData", "PostScript", \ "Graphics"], Cell[92448, 2772, 13898, 400, 186, 3830, 271, "GraphicsData", "PostScript", \ "Graphics"], Cell[106349, 3174, 13443, 384, 186, 3686, 259, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[119819, 3562, 183, 7, 31, "Text"], Cell[CellGroupData[{ Cell[120027, 3573, 113, 2, 70, "Input"], Cell[CellGroupData[{ Cell[120165, 3579, 22528, 662, 186, 7180, 468, "GraphicsData", "PostScript", \ "Graphics"], Cell[142696, 4243, 21049, 595, 186, 6339, 409, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[163772, 4842, 391, 13, 72, "Text"], Cell[CellGroupData[{ Cell[164188, 4859, 705, 13, 210, "Input"], Cell[CellGroupData[{ Cell[164918, 4876, 22060, 614, 186, 6388, 416, "GraphicsData", "PostScript", \ "Graphics"], Cell[186981, 5492, 20851, 572, 186, 5963, 384, "GraphicsData", "PostScript", \ "Graphics"], Cell[207835, 6066, 22679, 665, 186, 7201, 469, "GraphicsData", "PostScript", \ "Graphics"], Cell[230517, 6733, 21174, 598, 186, 6375, 411, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[251718, 7335, 1090, 29, 249, "Text"], Cell[CellGroupData[{ Cell[252833, 7368, 153, 3, 70, "Input"], Cell[252989, 7373, 38, 1, 49, "Output"] }, Open ]], Cell[253042, 7377, 376, 15, 52, "Text"], Cell[CellGroupData[{ Cell[253443, 7396, 85, 1, 50, "Input"], Cell[253531, 7399, 39, 1, 49, "Output"] }, Open ]], Cell[253585, 7403, 469, 10, 111, "Text"], Cell[CellGroupData[{ Cell[254079, 7417, 803, 15, 290, "Input"], Cell[CellGroupData[{ Cell[254907, 7436, 21519, 610, 186, 6454, 419, "GraphicsData", "PostScript", \ "Graphics"], Cell[276429, 8048, 20474, 569, 186, 6023, 386, "GraphicsData", "PostScript", \ "Graphics"], Cell[296906, 8619, 22242, 661, 186, 7267, 472, "GraphicsData", "PostScript", \ "Graphics"], Cell[319151, 9282, 20866, 596, 186, 6435, 413, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[340044, 9882, 327, 4, 90, "Text"], Cell[CellGroupData[{ Cell[340396, 9890, 58, 1, 50, "Input"], Cell[340457, 9893, 52, 1, 49, "Output"] }, Open ]], Cell[340524, 9897, 160, 2, 50, "Text"], Cell[340687, 9901, 163, 2, 26, "Text"] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)