(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 58922, 1478] NotebookOptionsPosition[ 54926, 1331] NotebookOutlinePosition[ 55305, 1347] CellTagsIndexPosition[ 55262, 1344] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Fun\[CCedilla]\[ATilde]o Geratriz. 17/10/2013, Vito R. Vanin\ \>", "Subsubtitle", CellChangeTimes->{{3.5910815708763084`*^9, 3.5910816004256496`*^9}}], Cell[CellGroupData[{ Cell["\<\ Geratrizes das fun\[CCedilla]\[OTilde]es mais comuns\ \>", "Section", CellChangeTimes->{{3.591081621021119*^9, 3.59108163120947*^9}}], Cell[CellGroupData[{ Cell["Binomial", "Subsubsection", CellChangeTimes->{{3.59108164127281*^9, 3.591081642476035*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PDF", "[", RowBox[{ RowBox[{"BinomialDistribution", "[", RowBox[{"m", ",", "p"}], "]"}], ",", "n"}], "]"}]], "Input", CellChangeTimes->{{3.5909405242388616`*^9, 3.590940529379484*^9}, { 3.590940623379456*^9, 3.5909406337388277`*^9}, {3.5909406841138124`*^9, 3.590940721426302*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\[Piecewise]", GridBox[{ { RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "p"}], ")"}], RowBox[{"m", "-", "n"}]], " ", SuperscriptBox["p", "n"], " ", RowBox[{"Binomial", "[", RowBox[{"m", ",", "n"}], "]"}]}], RowBox[{"0", "\[LessEqual]", "n", "\[LessEqual]", "m"}]}, {"0", TagBox["True", "PiecewiseDefault", AutoDelete->True]} }, AllowedDimensions->{2, Automatic}, Editable->True, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.84]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}, Selectable->True]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.35]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "Piecewise", DeleteWithContents->True, Editable->False, SelectWithContents->True, Selectable->False]], "Output", CellChangeTimes->{{3.590940705395054*^9, 3.5909407218637977`*^9}, 3.5909570536542606`*^9, 3.591081802583147*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GeneratingFunction", "[", RowBox[{ RowBox[{"PDF", "[", RowBox[{ RowBox[{"BinomialDistribution", "[", RowBox[{"m", ",", "p"}], "]"}], ",", "n"}], "]"}], ",", "n", ",", "t"}], "]"}]], "Input", CellChangeTimes->{{3.590940735785672*^9, 3.5909407530356674`*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\[Piecewise]", GridBox[{ { SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", RowBox[{"p", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "t"}], ")"}]}]}], ")"}], "m"], RowBox[{"m", "\[GreaterEqual]", "0"}]}, {"0", TagBox["True", "PiecewiseDefault", AutoDelete->True]} }, AllowedDimensions->{2, Automatic}, Editable->True, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.84]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}, Selectable->True]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.35]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "Piecewise", DeleteWithContents->True, Editable->False, SelectWithContents->True, Selectable->False]], "Output", CellChangeTimes->{3.5909407558169127`*^9, 3.5909570574357433`*^9, 3.5910818037394943`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Poisson", "Subsubsection", CellChangeTimes->{{3.5910816534769535`*^9, 3.5910816546801786`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", "a", "]"}], ",", "n"}], "]"}]], "Input", CellChangeTimes->{{3.5909409015043726`*^9, 3.5909409121293693`*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\[Piecewise]", GridBox[{ { FractionBox[ RowBox[{ SuperscriptBox["a", "n"], " ", SuperscriptBox["\[ExponentialE]", RowBox[{"-", "a"}]]}], RowBox[{"n", "!"}]], RowBox[{"n", "\[GreaterEqual]", "0"}]}, {"0", TagBox["True", "PiecewiseDefault", AutoDelete->True]} }, AllowedDimensions->{2, Automatic}, Editable->True, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.84]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}, Selectable->True]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.35]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "Piecewise", DeleteWithContents->True, Editable->False, SelectWithContents->True, Selectable->False]], "Output", CellChangeTimes->{3.590940916519991*^9, 3.5909570575138483`*^9, 3.591081803786374*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GeneratingFunction", "[", RowBox[{ RowBox[{"PDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", "a", "]"}], ",", "n"}], "]"}], ",", "n", ",", "t"}], "]"}]], "Input", CellChangeTimes->{{3.590940927723111*^9, 3.590940936394985*^9}}], Cell[BoxData[ SuperscriptBox["\[ExponentialE]", RowBox[{"a", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "t"}], ")"}]}]]], "Output", CellChangeTimes->{3.5909409380824833`*^9, 3.590957057982645*^9, 3.591081804052019*^9}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Propriedades elementares", "Section", CellChangeTimes->{{3.591081678807193*^9, 3.591081690792568*^9}}], Cell[CellGroupData[{ Cell["Probabilidade para i=0", "Subsubsection", CellChangeTimes->{{3.591081699746441*^9, 3.5910817062313566`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GeneratingFunction", "[", RowBox[{ RowBox[{"PDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", "a", "]"}], ",", "n"}], "]"}], ",", "n", ",", "0"}], "]"}]], "Input", CellChangeTimes->{{3.5909410641918235`*^9, 3.5909410645355735`*^9}}], Cell[BoxData[ SuperscriptBox["\[ExponentialE]", RowBox[{"-", "a"}]]], "Output", CellChangeTimes->{3.59094106634807*^9, 3.590957058138875*^9, 3.5910818041770296`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["normaliza\[CCedilla]\[ATilde]o", "Subsubsection", CellChangeTimes->{{3.5910817146226826`*^9, 3.5910817164353333`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GeneratingFunction", "[", RowBox[{ RowBox[{"PDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", "a", "]"}], ",", "n"}], "]"}], ",", "n", ",", "1"}], "]"}]], "Input", CellChangeTimes->{{3.59094107566057*^9, 3.59094107584807*^9}}], Cell[BoxData["1"], "Output", CellChangeTimes->{3.5909410766761923`*^9, 3.5909570582795057`*^9, 3.5910818042864146`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ recuperando a probabilidade para um i qualquer\ \>", "Subsection", CellChangeTimes->{{3.5910817265143003`*^9, 3.5910817360619717`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"prob", "[", "i_", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "t", "}"}], ",", RowBox[{ RowBox[{ RowBox[{"1", "/", RowBox[{"i", "!"}]}], " ", "\[IndentingNewLine]", RowBox[{"D", "[", RowBox[{ RowBox[{"GeneratingFunction", "[", RowBox[{ RowBox[{"PDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", "a", "]"}], ",", "n"}], "]"}], ",", "n", ",", "t"}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "i"}], "}"}]}], "]"}]}], "/.", RowBox[{"t", "\[Rule]", "0"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.5909411073011856`*^9, 3.5909411716917915`*^9}, { 3.590941263223014*^9, 3.590941333082364*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"prob", "[", "4", "]"}]], "Input", CellChangeTimes->{{3.590941174207412*^9, 3.5909411798792887`*^9}, { 3.5909413471761103`*^9, 3.590941347722989*^9}}], Cell[BoxData[ RowBox[{ FractionBox["1", "24"], " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[{"-", "a"}]]}]], "Output", CellChangeTimes->{ 3.5909411817386594`*^9, {3.590941339238613*^9, 3.5909413494886093`*^9}, 3.590957058435765*^9, 3.5910818044114246`*^9}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Aplica\[CCedilla]\[ATilde]o \[AGrave] soma de numeros aleat\[OAcute]rios - \ simula\[CCedilla]\[ATilde]o\ \>", "Section", CellChangeTimes->{{3.590957084468436*^9, 3.5909570961878138`*^9}, { 3.5910817451564817`*^9, 3.591081763626773*^9}}], Cell[CellGroupData[{ Cell["N\[UAcute]mero de termos constante", "Subsubsection", CellChangeTimes->{{3.5909571058289304`*^9, 3.5909571203922276`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"Total", "[", RowBox[{"RandomVariate", "[", RowBox[{ RowBox[{"BernoulliDistribution", "[", "0.1", "]"}], ",", "100"}], "]"}], "]"}], ",", RowBox[{"{", "10", "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.590957136299305*^9, 3.590957212678413*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "7", ",", "8", ",", "15", ",", "12", ",", "8", ",", "14", ",", "8", ",", "13", ",", "10", ",", "11"}], "}"}]], "Output", CellChangeTimes->{{3.5909571966150556`*^9, 3.5909572141784935`*^9}, 3.5910818044270515`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"sn", "[", RowBox[{"p_", ",", "n_"}], "]"}], ":=", RowBox[{"Total", "[", RowBox[{"RandomVariate", "[", RowBox[{ RowBox[{"BernoulliDistribution", "[", "p", "]"}], ",", "n"}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.590957221710119*^9, 3.59095725979031*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"simulsn", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"sn", "[", RowBox[{"0.1", ",", "100"}], "]"}], ",", RowBox[{"{", "100000", "}"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.5909572694470425`*^9, 3.590957312652491*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"hsn", "=", RowBox[{"Histogram", "[", "simulsn", "]"}]}]], "Input", CellChangeTimes->{{3.5909573182465286`*^9, 3.590957325090661*^9}, { 3.590957585370202*^9, 3.590957586917139*^9}}], Cell[BoxData[ GraphicsBox[ {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.504]], {}, {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.504]], RectangleBox[{0., 0}, {1., 2}, RoundingRadius->0], RectangleBox[{1., 0}, {2., 28}, RoundingRadius->0], RectangleBox[{2., 0}, {3., 177}, RoundingRadius->0], RectangleBox[{3., 0}, {4., 618}, RoundingRadius->0], RectangleBox[{4., 0}, {5., 1550}, RoundingRadius->0], RectangleBox[{5., 0}, {6., 3396}, RoundingRadius->0], RectangleBox[{6., 0}, {7., 6029}, RoundingRadius->0], RectangleBox[{7., 0}, {8., 8836}, RoundingRadius->0], RectangleBox[{8., 0}, {9., 11598}, RoundingRadius->0], RectangleBox[{9., 0}, {10., 13044}, RoundingRadius->0], RectangleBox[{10., 0}, {11., 13147}, RoundingRadius->0], RectangleBox[{11., 0}, {12., 11932}, RoundingRadius->0], RectangleBox[{12., 0}, {13., 9870}, RoundingRadius->0], RectangleBox[{13., 0}, {14., 7411}, RoundingRadius->0], RectangleBox[{14., 0}, {15., 5127}, RoundingRadius->0], RectangleBox[{15., 0}, {16., 3250}, RoundingRadius->0], RectangleBox[{16., 0}, {17., 1930}, RoundingRadius->0], RectangleBox[{17., 0}, {18., 1069}, RoundingRadius->0], RectangleBox[{18., 0}, {19., 553}, RoundingRadius->0], RectangleBox[{19., 0}, {20., 240}, RoundingRadius->0], RectangleBox[{20., 0}, {21., 103}, RoundingRadius->0], RectangleBox[{21., 0}, {22., 52}, RoundingRadius->0], RectangleBox[{22., 0}, {23., 24}, RoundingRadius->0], RectangleBox[{23., 0}, {24., 9}, RoundingRadius->0], RectangleBox[{24., 0}, RoundingRadius->0], RectangleBox[{25., 0}, {26., 2}, RoundingRadius->0], RectangleBox[{26., 0}, RoundingRadius->0], RectangleBox[{27., 0}, RoundingRadius->0]}, {}, {}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{0., 0}, FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, GridLines->{None, None}, PlotRange->{{0., 28.}, {All, All}}, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], Scaled[0.1]}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{3.5909573262157025`*^9, 3.5909575879796953`*^9, 3.591081806786624*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Mean", "[", "simulsn", "]"}], ",", RowBox[{"StandardDeviation", "[", "simulsn", "]"}]}], "}"}], "//", "N"}]], "Input", CellChangeTimes->{{3.590957330387805*^9, 3.590957363014575*^9}, { 3.591081975738229*^9, 3.5910819838326545`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"9.99236`", ",", "3.001751444659827`"}], "}"}]], "Output", CellChangeTimes->{{3.5909573539359355`*^9, 3.590957363702081*^9}, 3.5910818069116325`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"100", " ", "0.1", " ", "0.9"}], "]"}], " ", RowBox[{"(*", " ", RowBox[{"modelo", " ", "binomial", " ", "para", " ", "a", " ", RowBox[{"f", ".", "p", "."}]}], " ", "*)"}]}]], "Input", CellChangeTimes->{{3.590957375687107*^9, 3.5909573890628357`*^9}, { 3.591081988317404*^9, 3.591082002052925*^9}}], Cell[BoxData["3.`"], "Output", CellChangeTimes->{3.590957389453458*^9, 3.5910818069272594`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["N\[UAcute]mero de termos aleat\[OAcute]rio", "Subsubsection", CellChangeTimes->{{3.590958463167109*^9, 3.5909584797929974`*^9}, { 3.591081774518307*^9, 3.59108177497147*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"simulsnaleat", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"sn", "[", RowBox[{"0.1", ",", RowBox[{"RandomVariate", "[", RowBox[{"PoissonDistribution", "[", "100", "]"}], "]"}]}], "]"}], ",", RowBox[{"{", "100000", "}"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.5909574133297386`*^9, 3.590957464895005*^9}, 3.590957522210554*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Mean", "[", "simulsnaleat", "]"}], ",", RowBox[{"StandardDeviation", "[", "simulsnaleat", "]"}]}], "}"}], "//", "N"}]], "Input", CellChangeTimes->{{3.5909574803645897`*^9, 3.5909574875837326`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"9.99251`", ",", "3.1572984631225243`"}], "}"}]], "Output", CellChangeTimes->{3.5909574898338275`*^9, 3.590957556102992*^9, 3.5910818285540648`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"100", " ", "0.1"}], "]"}], " ", RowBox[{"(*", " ", RowBox[{"modelo", " ", "Poisson", " ", "para", " ", "a", " ", RowBox[{"f", ".", "p", "."}]}], " ", "*)"}]}]], "Input", CellChangeTimes->{{3.590957505600293*^9, 3.590957514319518*^9}, { 3.5910820120225077`*^9, 3.5910820223358684`*^9}}], Cell[BoxData["3.1622776601683795`"], "Output", CellChangeTimes->{3.5909575148039103`*^9, 3.5909575589937987`*^9, 3.5910818285540648`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"hsnaleat", "=", RowBox[{"Histogram", "[", "simulsnaleat", "]"}]}]], "Input", CellChangeTimes->{{3.590957570306902*^9, 3.5909575980271363`*^9}}], Cell[BoxData[ GraphicsBox[ {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.511]], {}, {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.511]], RectangleBox[{0., 0}, {1., 3}, RoundingRadius->0], RectangleBox[{1., 0}, {2., 39}, RoundingRadius->0], RectangleBox[{2., 0}, {3., 207}, RoundingRadius->0], RectangleBox[{3., 0}, {4., 790}, RoundingRadius->0], RectangleBox[{4., 0}, {5., 1875}, RoundingRadius->0], RectangleBox[{5., 0}, {6., 3889}, RoundingRadius->0], RectangleBox[{6., 0}, {7., 6295}, RoundingRadius->0], RectangleBox[{7., 0}, {8., 8959}, RoundingRadius->0], RectangleBox[{8., 0}, {9., 11195}, RoundingRadius->0], RectangleBox[{9., 0}, {10., 12604}, RoundingRadius->0], RectangleBox[{10., 0}, {11., 12538}, RoundingRadius->0], RectangleBox[{11., 0}, {12., 11356}, RoundingRadius->0], RectangleBox[{12., 0}, {13., 9510}, RoundingRadius->0], RectangleBox[{13., 0}, {14., 7249}, RoundingRadius->0], RectangleBox[{14., 0}, {15., 5230}, RoundingRadius->0], RectangleBox[{15., 0}, {16., 3421}, RoundingRadius->0], RectangleBox[{16., 0}, {17., 2154}, RoundingRadius->0], RectangleBox[{17., 0}, {18., 1299}, RoundingRadius->0], RectangleBox[{18., 0}, {19., 679}, RoundingRadius->0], RectangleBox[{19., 0}, {20., 372}, RoundingRadius->0], RectangleBox[{20., 0}, {21., 181}, RoundingRadius->0], RectangleBox[{21., 0}, {22., 86}, RoundingRadius->0], RectangleBox[{22., 0}, {23., 45}, RoundingRadius->0], RectangleBox[{23., 0}, {24., 16}, RoundingRadius->0], RectangleBox[{24., 0}, {25., 6}, RoundingRadius->0], RectangleBox[{25., 0}, RoundingRadius->0], RectangleBox[{26., 0}, RoundingRadius->0]}, {}, {}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{0., 0}, FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, GridLines->{None, None}, PlotRange->{{0., 27.}, {All, All}}, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], Scaled[0.1]}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.590957577776026*^9, 3.5909575987771482`*^9}, 3.5910818287415795`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Histogram", "[", RowBox[{"{", RowBox[{"simulsn", ",", "simulsnaleat"}], "}"}], "]"}]], "Input", CellChangeTimes->{{3.5909576012929068`*^9, 3.5909576144186363`*^9}, { 3.590957648389203*^9, 3.5909576840004835`*^9}, {3.590958430102832*^9, 3.5909584349937468`*^9}}], Cell[BoxData[ GraphicsBox[ {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.504]], {{}, {RGBColor[0.24720000000000014`, 0.24, 0.6], Opacity[0.5], EdgeForm[ Opacity[0.504]], RectangleBox[{0., 0.}, {1., 2}, RoundingRadius->0], RectangleBox[{1., 0.}, {2., 28}, RoundingRadius->0], RectangleBox[{2., 0.}, {3., 177}, RoundingRadius->0], RectangleBox[{3., 0.}, {4., 618}, RoundingRadius->0], RectangleBox[{4., 0.}, {5., 1550}, RoundingRadius->0], RectangleBox[{5., 0.}, {6., 3396}, RoundingRadius->0], RectangleBox[{6., 0.}, {7., 6029}, RoundingRadius->0], RectangleBox[{7., 0.}, {8., 8836}, RoundingRadius->0], RectangleBox[{8., 0.}, {9., 11598}, RoundingRadius->0], RectangleBox[{9., 0.}, {10., 13044}, RoundingRadius->0], RectangleBox[{10., 0.}, {11., 13147}, RoundingRadius->0], RectangleBox[{11., 0.}, {12., 11932}, RoundingRadius->0], RectangleBox[{12., 0.}, {13., 9870}, RoundingRadius->0], RectangleBox[{13., 0.}, {14., 7411}, RoundingRadius->0], RectangleBox[{14., 0.}, {15., 5127}, RoundingRadius->0], RectangleBox[{15., 0.}, {16., 3250}, RoundingRadius->0], RectangleBox[{16., 0.}, {17., 1930}, RoundingRadius->0], RectangleBox[{17., 0.}, {18., 1069}, RoundingRadius->0], RectangleBox[{18., 0.}, {19., 553}, RoundingRadius->0], RectangleBox[{19., 0.}, {20., 240}, RoundingRadius->0], RectangleBox[{20., 0.}, {21., 103}, RoundingRadius->0], RectangleBox[{21., 0.}, {22., 52}, RoundingRadius->0], RectangleBox[{22., 0.}, {23., 24}, RoundingRadius->0], RectangleBox[{23., 0.}, {24., 9}, RoundingRadius->0], RectangleBox[{24., 0.}, RoundingRadius->0], RectangleBox[{25., 0.}, {26., 2}, RoundingRadius->0], RectangleBox[{26., 0.}, RoundingRadius->0], RectangleBox[{27., 0.}, RoundingRadius->0]}, {}, {}}, {{}, {RGBColor[0.6, 0.24, 0.4428931686004542], Opacity[0.5], EdgeForm[Opacity[ 0.504]], RectangleBox[{0., 0.}, {1., 3}, RoundingRadius->0], RectangleBox[{1., 0.}, {2., 39}, RoundingRadius->0], RectangleBox[{2., 0.}, {3., 207}, RoundingRadius->0], RectangleBox[{3., 0.}, {4., 790}, RoundingRadius->0], RectangleBox[{4., 0.}, {5., 1875}, RoundingRadius->0], RectangleBox[{5., 0.}, {6., 3889}, RoundingRadius->0], RectangleBox[{6., 0.}, {7., 6295}, RoundingRadius->0], RectangleBox[{7., 0.}, {8., 8959}, RoundingRadius->0], RectangleBox[{8., 0.}, {9., 11195}, RoundingRadius->0], RectangleBox[{9., 0.}, {10., 12604}, RoundingRadius->0], RectangleBox[{10., 0.}, {11., 12538}, RoundingRadius->0], RectangleBox[{11., 0.}, {12., 11356}, RoundingRadius->0], RectangleBox[{12., 0.}, {13., 9510}, RoundingRadius->0], RectangleBox[{13., 0.}, {14., 7249}, RoundingRadius->0], RectangleBox[{14., 0.}, {15., 5230}, RoundingRadius->0], RectangleBox[{15., 0.}, {16., 3421}, RoundingRadius->0], RectangleBox[{16., 0.}, {17., 2154}, RoundingRadius->0], RectangleBox[{17., 0.}, {18., 1299}, RoundingRadius->0], RectangleBox[{18., 0.}, {19., 679}, RoundingRadius->0], RectangleBox[{19., 0.}, {20., 372}, RoundingRadius->0], RectangleBox[{20., 0.}, {21., 181}, RoundingRadius->0], RectangleBox[{21., 0.}, {22., 86}, RoundingRadius->0], RectangleBox[{22., 0.}, {23., 45}, RoundingRadius->0], RectangleBox[{23., 0.}, {24., 16}, RoundingRadius->0], RectangleBox[{24., 0.}, {25., 6}, RoundingRadius->0], RectangleBox[{25., 0.}, RoundingRadius->0], RectangleBox[{26., 0.}, RoundingRadius->0], RectangleBox[{27., 0.}, {28., 0}, RoundingRadius->0]}, {}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{0., 0}, FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, GridLines->{None, None}, ImageSize->{604.2856976450696, Automatic}, PlotRange->{{0., 28.}, {All, All}}, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], Scaled[0.1]}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.590957614668622*^9, {3.5909576626711884`*^9, 3.590957685234893*^9}, 3.5909584367594385`*^9, 3.591081829491643*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Histogram", "[", RowBox[{ RowBox[{"{", RowBox[{"simulsn", ",", "simulsnaleat"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{"0", ",", "1000"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.5909585739542828`*^9, 3.5909585911583476`*^9}}], Cell[BoxData[ GraphicsBox[ {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.504]], {{}, {RGBColor[0.24720000000000014`, 0.24, 0.6], Opacity[0.5], EdgeForm[ Opacity[0.504]], RectangleBox[{0., 0.}, {1., 2}, RoundingRadius->0], RectangleBox[{1., 0.}, {2., 28}, RoundingRadius->0], RectangleBox[{2., 0.}, {3., 177}, RoundingRadius->0], RectangleBox[{3., 0.}, {4., 618}, RoundingRadius->0], RectangleBox[{4., 0.}, {5., 1550}, RoundingRadius->0], RectangleBox[{5., 0.}, {6., 3396}, RoundingRadius->0], RectangleBox[{6., 0.}, {7., 6029}, RoundingRadius->0], RectangleBox[{7., 0.}, {8., 8836}, RoundingRadius->0], RectangleBox[{8., 0.}, {9., 11598}, RoundingRadius->0], RectangleBox[{9., 0.}, {10., 13044}, RoundingRadius->0], RectangleBox[{10., 0.}, {11., 13147}, RoundingRadius->0], RectangleBox[{11., 0.}, {12., 11932}, RoundingRadius->0], RectangleBox[{12., 0.}, {13., 9870}, RoundingRadius->0], RectangleBox[{13., 0.}, {14., 7411}, RoundingRadius->0], RectangleBox[{14., 0.}, {15., 5127}, RoundingRadius->0], RectangleBox[{15., 0.}, {16., 3250}, RoundingRadius->0], RectangleBox[{16., 0.}, {17., 1930}, RoundingRadius->0], RectangleBox[{17., 0.}, {18., 1069}, RoundingRadius->0], RectangleBox[{18., 0.}, {19., 553}, RoundingRadius->0], RectangleBox[{19., 0.}, {20., 240}, RoundingRadius->0], RectangleBox[{20., 0.}, {21., 103}, RoundingRadius->0], RectangleBox[{21., 0.}, {22., 52}, RoundingRadius->0], RectangleBox[{22., 0.}, {23., 24}, RoundingRadius->0], RectangleBox[{23., 0.}, {24., 9}, RoundingRadius->0], RectangleBox[{24., 0.}, RoundingRadius->0], RectangleBox[{25., 0.}, {26., 2}, RoundingRadius->0], RectangleBox[{26., 0.}, RoundingRadius->0], RectangleBox[{27., 0.}, RoundingRadius->0]}, {}, {}}, {{}, {RGBColor[0.6, 0.24, 0.4428931686004542], Opacity[0.5], EdgeForm[Opacity[ 0.504]], RectangleBox[{0., 0.}, {1., 3}, RoundingRadius->0], RectangleBox[{1., 0.}, {2., 39}, RoundingRadius->0], RectangleBox[{2., 0.}, {3., 207}, RoundingRadius->0], RectangleBox[{3., 0.}, {4., 790}, RoundingRadius->0], RectangleBox[{4., 0.}, {5., 1875}, RoundingRadius->0], RectangleBox[{5., 0.}, {6., 3889}, RoundingRadius->0], RectangleBox[{6., 0.}, {7., 6295}, RoundingRadius->0], RectangleBox[{7., 0.}, {8., 8959}, RoundingRadius->0], RectangleBox[{8., 0.}, {9., 11195}, RoundingRadius->0], RectangleBox[{9., 0.}, {10., 12604}, RoundingRadius->0], RectangleBox[{10., 0.}, {11., 12538}, RoundingRadius->0], RectangleBox[{11., 0.}, {12., 11356}, RoundingRadius->0], RectangleBox[{12., 0.}, {13., 9510}, RoundingRadius->0], RectangleBox[{13., 0.}, {14., 7249}, RoundingRadius->0], RectangleBox[{14., 0.}, {15., 5230}, RoundingRadius->0], RectangleBox[{15., 0.}, {16., 3421}, RoundingRadius->0], RectangleBox[{16., 0.}, {17., 2154}, RoundingRadius->0], RectangleBox[{17., 0.}, {18., 1299}, RoundingRadius->0], RectangleBox[{18., 0.}, {19., 679}, RoundingRadius->0], RectangleBox[{19., 0.}, {20., 372}, RoundingRadius->0], RectangleBox[{20., 0.}, {21., 181}, RoundingRadius->0], RectangleBox[{21., 0.}, {22., 86}, RoundingRadius->0], RectangleBox[{22., 0.}, {23., 45}, RoundingRadius->0], RectangleBox[{23., 0.}, {24., 16}, RoundingRadius->0], RectangleBox[{24., 0.}, {25., 6}, RoundingRadius->0], RectangleBox[{25., 0.}, RoundingRadius->0], RectangleBox[{26., 0.}, RoundingRadius->0], RectangleBox[{27., 0.}, {28., 0}, RoundingRadius->0]}, {}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{0., 0}, FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, GridLines->{None, None}, PlotRange->{{0., 28.}, {0, 1000}}, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, {0, 0}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.590958584642344*^9, 3.5909585926740217`*^9}, 3.591081830257332*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ as diferen\[CCedilla]as entre soma com n\[UAcute]mero de termos fixo e aleat\ \[OAcute]rio crescem com a probabilidade do evento\ \>", "Subsubsection", CellChangeTimes->{{3.590958492824947*^9, 3.5909585132010365`*^9}, { 3.591082030977215*^9, 3.59108204529091*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"simulsn2", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"sn", "[", RowBox[{"0.5", ",", "100"}], "]"}], ",", RowBox[{"{", "10000", "}"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.5909577725364437`*^9, 3.5909577861778107`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Histogram", "[", "simulsn2", "]"}]], "Input", CellChangeTimes->{{3.590957817273208*^9, 3.5909578188514366`*^9}, { 3.590958310565199*^9, 3.5909583132684937`*^9}, {3.590958519967022*^9, 3.590958520654577*^9}}], Cell[BoxData[ GraphicsBox[ {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.44099999999999995`]], {}, {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.44099999999999995`]], RectangleBox[{34., 0}, {35., 4}, RoundingRadius->0], RectangleBox[{35., 0}, {36., 9}, RoundingRadius->0], RectangleBox[{36., 0}, {37., 9}, RoundingRadius->0], RectangleBox[{37., 0}, {38., 19}, RoundingRadius->0], RectangleBox[{38., 0}, {39., 43}, RoundingRadius->0], RectangleBox[{39., 0}, {40., 68}, RoundingRadius->0], RectangleBox[{40., 0}, {41., 91}, RoundingRadius->0], RectangleBox[{41., 0}, {42., 145}, RoundingRadius->0], RectangleBox[{42., 0}, {43., 243}, RoundingRadius->0], RectangleBox[{43., 0}, {44., 327}, RoundingRadius->0], RectangleBox[{44., 0}, {45., 374}, RoundingRadius->0], RectangleBox[{45., 0}, {46., 519}, RoundingRadius->0], RectangleBox[{46., 0}, {47., 536}, RoundingRadius->0], RectangleBox[{47., 0}, {48., 693}, RoundingRadius->0], RectangleBox[{48., 0}, {49., 735}, RoundingRadius->0], RectangleBox[{49., 0}, {50., 769}, RoundingRadius->0], RectangleBox[{50., 0}, {51., 773}, RoundingRadius->0], RectangleBox[{51., 0}, {52., 811}, RoundingRadius->0], RectangleBox[{52., 0}, {53., 750}, RoundingRadius->0], RectangleBox[{53., 0}, {54., 643}, RoundingRadius->0], RectangleBox[{54., 0}, {55., 586}, RoundingRadius->0], RectangleBox[{55., 0}, {56., 478}, RoundingRadius->0], RectangleBox[{56., 0}, {57., 376}, RoundingRadius->0], RectangleBox[{57., 0}, {58., 329}, RoundingRadius->0], RectangleBox[{58., 0}, {59., 213}, RoundingRadius->0], RectangleBox[{59., 0}, {60., 162}, RoundingRadius->0], RectangleBox[{60., 0}, {61., 116}, RoundingRadius->0], RectangleBox[{61., 0}, {62., 65}, RoundingRadius->0], RectangleBox[{62., 0}, {63., 56}, RoundingRadius->0], RectangleBox[{63., 0}, {64., 26}, RoundingRadius->0], RectangleBox[{64., 0}, {65., 21}, RoundingRadius->0], RectangleBox[{65., 0}, {66., 4}, RoundingRadius->0], RectangleBox[{66., 0}, {67., 3}, RoundingRadius->0], RectangleBox[{67., 0}, RoundingRadius->0], RectangleBox[{68., 0}, RoundingRadius->0], RectangleBox[{69., 0}, RoundingRadius->0], RectangleBox[{70., 0}, RoundingRadius->0]}, {}, {}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{34., 0}, FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, GridLines->{None, None}, PlotRange->{{34., 71.}, {All, All}}, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], Scaled[0.1]}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{3.590957820288988*^9, 3.5909585226859074`*^9, 3.5910818304761*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Mean", "[", "simulsn2", "]"}], ",", RowBox[{"StandardDeviation", "[", "simulsn2", "]"}]}], "}"}], "//", "N"}]], "Input", CellChangeTimes->{{3.5909578345397797`*^9, 3.5909578358210897`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"50.0471`", ",", "4.962292214733272`"}], "}"}]], "Output", CellChangeTimes->{3.590957836946129*^9, 3.591081830491829*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Sqrt", "[", RowBox[{"100", " ", "0.5", " ", "0.5"}], "]"}]], "Input", CellChangeTimes->{{3.5909578399619436`*^9, 3.590957850915656*^9}}], Cell[BoxData["5.`"], "Output", CellChangeTimes->{3.5909578514781847`*^9, 3.591081830507354*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"simulsnaleat2", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"sn", "[", RowBox[{"0.5", ",", RowBox[{"RandomVariate", "[", RowBox[{"PoissonDistribution", "[", "100", "]"}], "]"}]}], "]"}], ",", RowBox[{"{", "10000", "}"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.5909578708541994`*^9, 3.590957877526452*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Mean", "[", "simulsnaleat2", "]"}], ",", RowBox[{"StandardDeviation", "[", "simulsnaleat2", "]"}]}], "}"}], "//", "N"}]], "Input", CellChangeTimes->{{3.5909582119036694`*^9, 3.590958213388155*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"49.9956`", ",", "7.115296436856193`"}], "}"}]], "Output", CellChangeTimes->{3.590958215263226*^9, 3.591081832710663*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Histogram", "[", "simulsnaleat2", "]"}]], "Input", CellChangeTimes->{{3.5909582316391087`*^9, 3.5909582331704416`*^9}, { 3.590958317409318*^9, 3.5909583533643847`*^9}, 3.5909585276080728`*^9}], Cell[BoxData[ GraphicsBox[ {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.32899999999999996`]], {}, {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.32899999999999996`]], RectangleBox[{25., 0}, RoundingRadius->0], RectangleBox[{26., 0}, RoundingRadius->0], RectangleBox[{27., 0}, RoundingRadius->0], RectangleBox[{28., 0}, {29., 5}, RoundingRadius->0], RectangleBox[{29., 0}, {30., 4}, RoundingRadius->0], RectangleBox[{30., 0}, {31., 6}, RoundingRadius->0], RectangleBox[{31., 0}, {32., 10}, RoundingRadius->0], RectangleBox[{32., 0}, {33., 18}, RoundingRadius->0], RectangleBox[{33., 0}, {34., 18}, RoundingRadius->0], RectangleBox[{34., 0}, {35., 37}, RoundingRadius->0], RectangleBox[{35., 0}, {36., 49}, RoundingRadius->0], RectangleBox[{36., 0}, {37., 88}, RoundingRadius->0], RectangleBox[{37., 0}, {38., 110}, RoundingRadius->0], RectangleBox[{38., 0}, {39., 142}, RoundingRadius->0], RectangleBox[{39., 0}, {40., 172}, RoundingRadius->0], RectangleBox[{40., 0}, {41., 227}, RoundingRadius->0], RectangleBox[{41., 0}, {42., 257}, RoundingRadius->0], RectangleBox[{42., 0}, {43., 321}, RoundingRadius->0], RectangleBox[{43., 0}, {44., 315}, RoundingRadius->0], RectangleBox[{44., 0}, {45., 428}, RoundingRadius->0], RectangleBox[{45., 0}, {46., 475}, RoundingRadius->0], RectangleBox[{46., 0}, {47., 484}, RoundingRadius->0], RectangleBox[{47., 0}, {48., 520}, RoundingRadius->0], RectangleBox[{48., 0}, {49., 545}, RoundingRadius->0], RectangleBox[{49., 0}, {50., 593}, RoundingRadius->0], RectangleBox[{50., 0}, {51., 595}, RoundingRadius->0], RectangleBox[{51., 0}, {52., 540}, RoundingRadius->0], RectangleBox[{52., 0}, {53., 527}, RoundingRadius->0], RectangleBox[{53., 0}, {54., 471}, RoundingRadius->0], RectangleBox[{54., 0}, {55., 463}, RoundingRadius->0], RectangleBox[{55., 0}, {56., 431}, RoundingRadius->0], RectangleBox[{56., 0}, {57., 360}, RoundingRadius->0], RectangleBox[{57., 0}, {58., 300}, RoundingRadius->0], RectangleBox[{58., 0}, {59., 291}, RoundingRadius->0], RectangleBox[{59., 0}, {60., 271}, RoundingRadius->0], RectangleBox[{60., 0}, {61., 209}, RoundingRadius->0], RectangleBox[{61., 0}, {62., 164}, RoundingRadius->0], RectangleBox[{62., 0}, {63., 115}, RoundingRadius->0], RectangleBox[{63., 0}, {64., 88}, RoundingRadius->0], RectangleBox[{64., 0}, {65., 98}, RoundingRadius->0], RectangleBox[{65., 0}, {66., 61}, RoundingRadius->0], RectangleBox[{66., 0}, {67., 51}, RoundingRadius->0], RectangleBox[{67., 0}, {68., 33}, RoundingRadius->0], RectangleBox[{68., 0}, {69., 35}, RoundingRadius->0], RectangleBox[{69., 0}, {70., 22}, RoundingRadius->0], RectangleBox[{70., 0}, {71., 14}, RoundingRadius->0], RectangleBox[{71., 0}, {72., 14}, RoundingRadius->0], RectangleBox[{72., 0}, {73., 9}, RoundingRadius->0], RectangleBox[{73., 0}, {74., 3}, RoundingRadius->0], RectangleBox[{74., 0}, RoundingRadius->0], RectangleBox[{75., 0}, RoundingRadius->0], RectangleBox[{76., 0}, {77., 2}, RoundingRadius->0], RectangleBox[{78., 0}, {79., 4}, RoundingRadius->0]}, {}, {}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{25., 0}, FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, GridLines->{None, None}, PlotRange->{{25., 79.}, {All, All}}, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], Scaled[0.1]}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{3.5909582349205256`*^9, 3.590958528186201*^9, 3.5910818327731676`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Histogram", "[", RowBox[{"{", RowBox[{"simulsn2", ",", "simulsnaleat2"}], "}"}], "]"}]], "Input", CellChangeTimes->{{3.590958253218389*^9, 3.59095828600138*^9}, { 3.590958376084319*^9, 3.5909584069922223`*^9}}], Cell[BoxData[ GraphicsBox[ {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.322]], {{}, {RGBColor[0.24720000000000014`, 0.24, 0.6], Opacity[0.5], EdgeForm[ Opacity[0.322]], RectangleBox[{25., 0.}, {26., 0}, RoundingRadius->0], RectangleBox[{26., 0.}, {27., 0}, RoundingRadius->0], RectangleBox[{27., 0.}, {28., 0}, RoundingRadius->0], RectangleBox[{28., 0.}, {29., 0}, RoundingRadius->0], RectangleBox[{29., 0.}, {30., 0}, RoundingRadius->0], RectangleBox[{30., 0.}, {31., 0}, RoundingRadius->0], RectangleBox[{31., 0.}, {32., 0}, RoundingRadius->0], RectangleBox[{32., 0.}, {33., 0}, RoundingRadius->0], RectangleBox[{33., 0.}, {34., 0}, RoundingRadius->0], RectangleBox[{34., 0.}, {35., 4}, RoundingRadius->0], RectangleBox[{35., 0.}, {36., 9}, RoundingRadius->0], RectangleBox[{36., 0.}, {37., 9}, RoundingRadius->0], RectangleBox[{37., 0.}, {38., 19}, RoundingRadius->0], RectangleBox[{38., 0.}, {39., 43}, RoundingRadius->0], RectangleBox[{39., 0.}, {40., 68}, RoundingRadius->0], RectangleBox[{40., 0.}, {41., 91}, RoundingRadius->0], RectangleBox[{41., 0.}, {42., 145}, RoundingRadius->0], RectangleBox[{42., 0.}, {43., 243}, RoundingRadius->0], RectangleBox[{43., 0.}, {44., 327}, RoundingRadius->0], RectangleBox[{44., 0.}, {45., 374}, RoundingRadius->0], RectangleBox[{45., 0.}, {46., 519}, RoundingRadius->0], RectangleBox[{46., 0.}, {47., 536}, RoundingRadius->0], RectangleBox[{47., 0.}, {48., 693}, RoundingRadius->0], RectangleBox[{48., 0.}, {49., 735}, RoundingRadius->0], RectangleBox[{49., 0.}, {50., 769}, RoundingRadius->0], RectangleBox[{50., 0.}, {51., 773}, RoundingRadius->0], RectangleBox[{51., 0.}, {52., 811}, RoundingRadius->0], RectangleBox[{52., 0.}, {53., 750}, RoundingRadius->0], RectangleBox[{53., 0.}, {54., 643}, RoundingRadius->0], RectangleBox[{54., 0.}, {55., 586}, RoundingRadius->0], RectangleBox[{55., 0.}, {56., 478}, RoundingRadius->0], RectangleBox[{56., 0.}, {57., 376}, RoundingRadius->0], RectangleBox[{57., 0.}, {58., 329}, RoundingRadius->0], RectangleBox[{58., 0.}, {59., 213}, RoundingRadius->0], RectangleBox[{59., 0.}, {60., 162}, RoundingRadius->0], RectangleBox[{60., 0.}, {61., 116}, RoundingRadius->0], RectangleBox[{61., 0.}, {62., 65}, RoundingRadius->0], RectangleBox[{62., 0.}, {63., 56}, RoundingRadius->0], RectangleBox[{63., 0.}, {64., 26}, RoundingRadius->0], RectangleBox[{64., 0.}, {65., 21}, RoundingRadius->0], RectangleBox[{65., 0.}, {66., 4}, RoundingRadius->0], RectangleBox[{66., 0.}, {67., 3}, RoundingRadius->0], RectangleBox[{67., 0.}, RoundingRadius->0], RectangleBox[{68., 0.}, RoundingRadius->0], RectangleBox[{69., 0.}, RoundingRadius->0], RectangleBox[{70., 0.}, RoundingRadius->0], RectangleBox[{71., 0.}, {72., 0}, RoundingRadius->0], RectangleBox[{72., 0.}, {73., 0}, RoundingRadius->0], RectangleBox[{73., 0.}, {74., 0}, RoundingRadius->0], RectangleBox[{74., 0.}, {75., 0}, RoundingRadius->0], RectangleBox[{75., 0.}, {76., 0}, RoundingRadius->0], RectangleBox[{76., 0.}, {77., 0}, RoundingRadius->0], RectangleBox[{77., 0.}, {78., 0}, RoundingRadius->0], RectangleBox[{78., 0.}, {79., 0}, RoundingRadius->0]}, {}, {}}, {{}, {RGBColor[0.6, 0.24, 0.4428931686004542], Opacity[0.5], EdgeForm[Opacity[ 0.322]], RectangleBox[{25., 0.}, RoundingRadius->0], RectangleBox[{26., 0.}, RoundingRadius->0], RectangleBox[{27., 0.}, RoundingRadius->0], RectangleBox[{28., 0.}, {29., 5}, RoundingRadius->0], RectangleBox[{29., 0.}, {30., 4}, RoundingRadius->0], RectangleBox[{30., 0.}, {31., 6}, RoundingRadius->0], RectangleBox[{31., 0.}, {32., 10}, RoundingRadius->0], RectangleBox[{32., 0.}, {33., 18}, RoundingRadius->0], RectangleBox[{33., 0.}, {34., 18}, RoundingRadius->0], RectangleBox[{34., 0.}, {35., 37}, RoundingRadius->0], RectangleBox[{35., 0.}, {36., 49}, RoundingRadius->0], RectangleBox[{36., 0.}, {37., 88}, RoundingRadius->0], RectangleBox[{37., 0.}, {38., 110}, RoundingRadius->0], RectangleBox[{38., 0.}, {39., 142}, RoundingRadius->0], RectangleBox[{39., 0.}, {40., 172}, RoundingRadius->0], RectangleBox[{40., 0.}, {41., 227}, RoundingRadius->0], RectangleBox[{41., 0.}, {42., 257}, RoundingRadius->0], RectangleBox[{42., 0.}, {43., 321}, RoundingRadius->0], RectangleBox[{43., 0.}, {44., 315}, RoundingRadius->0], RectangleBox[{44., 0.}, {45., 428}, RoundingRadius->0], RectangleBox[{45., 0.}, {46., 475}, RoundingRadius->0], RectangleBox[{46., 0.}, {47., 484}, RoundingRadius->0], RectangleBox[{47., 0.}, {48., 520}, RoundingRadius->0], RectangleBox[{48., 0.}, {49., 545}, RoundingRadius->0], RectangleBox[{49., 0.}, {50., 593}, RoundingRadius->0], RectangleBox[{50., 0.}, {51., 595}, RoundingRadius->0], RectangleBox[{51., 0.}, {52., 540}, RoundingRadius->0], RectangleBox[{52., 0.}, {53., 527}, RoundingRadius->0], RectangleBox[{53., 0.}, {54., 471}, RoundingRadius->0], RectangleBox[{54., 0.}, {55., 463}, RoundingRadius->0], RectangleBox[{55., 0.}, {56., 431}, RoundingRadius->0], RectangleBox[{56., 0.}, {57., 360}, RoundingRadius->0], RectangleBox[{57., 0.}, {58., 300}, RoundingRadius->0], RectangleBox[{58., 0.}, {59., 291}, RoundingRadius->0], RectangleBox[{59., 0.}, {60., 271}, RoundingRadius->0], RectangleBox[{60., 0.}, {61., 209}, RoundingRadius->0], RectangleBox[{61., 0.}, {62., 164}, RoundingRadius->0], RectangleBox[{62., 0.}, {63., 115}, RoundingRadius->0], RectangleBox[{63., 0.}, {64., 88}, RoundingRadius->0], RectangleBox[{64., 0.}, {65., 98}, RoundingRadius->0], RectangleBox[{65., 0.}, {66., 61}, RoundingRadius->0], RectangleBox[{66., 0.}, {67., 51}, RoundingRadius->0], RectangleBox[{67., 0.}, {68., 33}, RoundingRadius->0], RectangleBox[{68., 0.}, {69., 35}, RoundingRadius->0], RectangleBox[{69., 0.}, {70., 22}, RoundingRadius->0], RectangleBox[{70., 0.}, {71., 14}, RoundingRadius->0], RectangleBox[{71., 0.}, {72., 14}, RoundingRadius->0], RectangleBox[{72., 0.}, {73., 9}, RoundingRadius->0], RectangleBox[{73., 0.}, {74., 3}, RoundingRadius->0], RectangleBox[{74., 0.}, RoundingRadius->0], RectangleBox[{75., 0.}, RoundingRadius->0], RectangleBox[{76., 0.}, {77., 2}, RoundingRadius->0], RectangleBox[{77., 0.}, {78., 0}, RoundingRadius->0], RectangleBox[{78., 0.}, {79., 4}, RoundingRadius->0]}, {}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{25., 0}, FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, GridLines->{None, None}, PlotRange->{{25., 79.}, {All, All}}, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], Scaled[0.1]}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.5909582558278933`*^9, 3.5909582864701557`*^9}, { 3.590958383959743*^9, 3.590958408945451*^9}, 3.5910818329294305`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Histogram", "[", RowBox[{ RowBox[{"{", RowBox[{"simulsn2", ",", "simulsnaleat2"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{"0", ",", "200"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.590958542405736*^9, 3.590958551593711*^9}}], Cell[BoxData[ GraphicsBox[ {RGBColor[0.798413061722744, 0.824719615472648, 0.968322270542458], EdgeForm[Opacity[0.322]], {{}, {RGBColor[0.24720000000000014`, 0.24, 0.6], Opacity[0.5], EdgeForm[ Opacity[0.322]], RectangleBox[{25., 0.}, {26., 0}, RoundingRadius->0], RectangleBox[{26., 0.}, {27., 0}, RoundingRadius->0], RectangleBox[{27., 0.}, {28., 0}, RoundingRadius->0], RectangleBox[{28., 0.}, {29., 0}, RoundingRadius->0], RectangleBox[{29., 0.}, {30., 0}, RoundingRadius->0], RectangleBox[{30., 0.}, {31., 0}, RoundingRadius->0], RectangleBox[{31., 0.}, {32., 0}, RoundingRadius->0], RectangleBox[{32., 0.}, {33., 0}, RoundingRadius->0], RectangleBox[{33., 0.}, {34., 0}, RoundingRadius->0], RectangleBox[{34., 0.}, {35., 4}, RoundingRadius->0], RectangleBox[{35., 0.}, {36., 9}, RoundingRadius->0], RectangleBox[{36., 0.}, {37., 9}, RoundingRadius->0], RectangleBox[{37., 0.}, {38., 19}, RoundingRadius->0], RectangleBox[{38., 0.}, {39., 43}, RoundingRadius->0], RectangleBox[{39., 0.}, {40., 68}, RoundingRadius->0], RectangleBox[{40., 0.}, {41., 91}, RoundingRadius->0], RectangleBox[{41., 0.}, {42., 145}, RoundingRadius->0], RectangleBox[{42., 0.}, {43., 243}, RoundingRadius->0], RectangleBox[{43., 0.}, {44., 327}, RoundingRadius->0], RectangleBox[{44., 0.}, {45., 374}, RoundingRadius->0], RectangleBox[{45., 0.}, {46., 519}, RoundingRadius->0], RectangleBox[{46., 0.}, {47., 536}, RoundingRadius->0], RectangleBox[{47., 0.}, {48., 693}, RoundingRadius->0], RectangleBox[{48., 0.}, {49., 735}, RoundingRadius->0], RectangleBox[{49., 0.}, {50., 769}, RoundingRadius->0], RectangleBox[{50., 0.}, {51., 773}, RoundingRadius->0], RectangleBox[{51., 0.}, {52., 811}, RoundingRadius->0], RectangleBox[{52., 0.}, {53., 750}, RoundingRadius->0], RectangleBox[{53., 0.}, {54., 643}, RoundingRadius->0], RectangleBox[{54., 0.}, {55., 586}, RoundingRadius->0], RectangleBox[{55., 0.}, {56., 478}, RoundingRadius->0], RectangleBox[{56., 0.}, {57., 376}, RoundingRadius->0], RectangleBox[{57., 0.}, {58., 329}, RoundingRadius->0], RectangleBox[{58., 0.}, {59., 213}, RoundingRadius->0], RectangleBox[{59., 0.}, {60., 162}, RoundingRadius->0], RectangleBox[{60., 0.}, {61., 116}, RoundingRadius->0], RectangleBox[{61., 0.}, {62., 65}, RoundingRadius->0], RectangleBox[{62., 0.}, {63., 56}, RoundingRadius->0], RectangleBox[{63., 0.}, {64., 26}, RoundingRadius->0], RectangleBox[{64., 0.}, {65., 21}, RoundingRadius->0], RectangleBox[{65., 0.}, {66., 4}, RoundingRadius->0], RectangleBox[{66., 0.}, {67., 3}, RoundingRadius->0], RectangleBox[{67., 0.}, RoundingRadius->0], RectangleBox[{68., 0.}, RoundingRadius->0], RectangleBox[{69., 0.}, RoundingRadius->0], RectangleBox[{70., 0.}, RoundingRadius->0], RectangleBox[{71., 0.}, {72., 0}, RoundingRadius->0], RectangleBox[{72., 0.}, {73., 0}, RoundingRadius->0], RectangleBox[{73., 0.}, {74., 0}, RoundingRadius->0], RectangleBox[{74., 0.}, {75., 0}, RoundingRadius->0], RectangleBox[{75., 0.}, {76., 0}, RoundingRadius->0], RectangleBox[{76., 0.}, {77., 0}, RoundingRadius->0], RectangleBox[{77., 0.}, {78., 0}, RoundingRadius->0], RectangleBox[{78., 0.}, {79., 0}, RoundingRadius->0]}, {}, {}}, {{}, {RGBColor[0.6, 0.24, 0.4428931686004542], Opacity[0.5], EdgeForm[Opacity[ 0.322]], RectangleBox[{25., 0.}, RoundingRadius->0], RectangleBox[{26., 0.}, RoundingRadius->0], RectangleBox[{27., 0.}, RoundingRadius->0], RectangleBox[{28., 0.}, {29., 5}, RoundingRadius->0], RectangleBox[{29., 0.}, {30., 4}, RoundingRadius->0], RectangleBox[{30., 0.}, {31., 6}, RoundingRadius->0], RectangleBox[{31., 0.}, {32., 10}, RoundingRadius->0], RectangleBox[{32., 0.}, {33., 18}, RoundingRadius->0], RectangleBox[{33., 0.}, {34., 18}, RoundingRadius->0], RectangleBox[{34., 0.}, {35., 37}, RoundingRadius->0], RectangleBox[{35., 0.}, {36., 49}, RoundingRadius->0], RectangleBox[{36., 0.}, {37., 88}, RoundingRadius->0], RectangleBox[{37., 0.}, {38., 110}, RoundingRadius->0], RectangleBox[{38., 0.}, {39., 142}, RoundingRadius->0], RectangleBox[{39., 0.}, {40., 172}, RoundingRadius->0], RectangleBox[{40., 0.}, {41., 227}, RoundingRadius->0], RectangleBox[{41., 0.}, {42., 257}, RoundingRadius->0], RectangleBox[{42., 0.}, {43., 321}, RoundingRadius->0], RectangleBox[{43., 0.}, {44., 315}, RoundingRadius->0], RectangleBox[{44., 0.}, {45., 428}, RoundingRadius->0], RectangleBox[{45., 0.}, {46., 475}, RoundingRadius->0], RectangleBox[{46., 0.}, {47., 484}, RoundingRadius->0], RectangleBox[{47., 0.}, {48., 520}, RoundingRadius->0], RectangleBox[{48., 0.}, {49., 545}, RoundingRadius->0], RectangleBox[{49., 0.}, {50., 593}, RoundingRadius->0], RectangleBox[{50., 0.}, {51., 595}, RoundingRadius->0], RectangleBox[{51., 0.}, {52., 540}, RoundingRadius->0], RectangleBox[{52., 0.}, {53., 527}, RoundingRadius->0], RectangleBox[{53., 0.}, {54., 471}, RoundingRadius->0], RectangleBox[{54., 0.}, {55., 463}, RoundingRadius->0], RectangleBox[{55., 0.}, {56., 431}, RoundingRadius->0], RectangleBox[{56., 0.}, {57., 360}, RoundingRadius->0], RectangleBox[{57., 0.}, {58., 300}, RoundingRadius->0], RectangleBox[{58., 0.}, {59., 291}, RoundingRadius->0], RectangleBox[{59., 0.}, {60., 271}, RoundingRadius->0], RectangleBox[{60., 0.}, {61., 209}, RoundingRadius->0], RectangleBox[{61., 0.}, {62., 164}, RoundingRadius->0], RectangleBox[{62., 0.}, {63., 115}, RoundingRadius->0], RectangleBox[{63., 0.}, {64., 88}, RoundingRadius->0], RectangleBox[{64., 0.}, {65., 98}, RoundingRadius->0], RectangleBox[{65., 0.}, {66., 61}, RoundingRadius->0], RectangleBox[{66., 0.}, {67., 51}, RoundingRadius->0], RectangleBox[{67., 0.}, {68., 33}, RoundingRadius->0], RectangleBox[{68., 0.}, {69., 35}, RoundingRadius->0], RectangleBox[{69., 0.}, {70., 22}, RoundingRadius->0], RectangleBox[{70., 0.}, {71., 14}, RoundingRadius->0], RectangleBox[{71., 0.}, {72., 14}, RoundingRadius->0], RectangleBox[{72., 0.}, {73., 9}, RoundingRadius->0], RectangleBox[{73., 0.}, {74., 3}, RoundingRadius->0], RectangleBox[{74., 0.}, RoundingRadius->0], RectangleBox[{75., 0.}, RoundingRadius->0], RectangleBox[{76., 0.}, {77., 2}, RoundingRadius->0], RectangleBox[{77., 0.}, {78., 0}, RoundingRadius->0], RectangleBox[{78., 0.}, {79., 4}, RoundingRadius->0]}, {}, {}}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{25., 0}, FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, GridLines->{None, None}, PlotRange->{{25., 79.}, {0, 200}}, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, {0, 0}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{3.590958552140606*^9, 3.5910818330856934`*^9}] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, WindowSize->{1277, 729}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, Magnification->1.4000000953674316`, FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (January 25, 2013)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[579, 22, 161, 3, 45, "Subsubtitle"], Cell[CellGroupData[{ Cell[765, 29, 144, 3, 118, "Section"], Cell[CellGroupData[{ Cell[934, 36, 98, 1, 54, "Subsubsection"], Cell[CellGroupData[{ Cell[1057, 41, 322, 7, 42, "Input"], Cell[1382, 50, 1910, 54, 60, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3329, 109, 308, 8, 42, "Input"], Cell[3640, 119, 1821, 53, 60, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[5510, 178, 102, 1, 54, "Subsubsection"], Cell[CellGroupData[{ Cell[5637, 183, 196, 4, 42, "Input"], Cell[5836, 189, 1784, 52, 74, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7657, 246, 279, 7, 42, "Input"], Cell[7939, 255, 249, 7, 43, "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[8249, 269, 109, 1, 118, "Section"], Cell[CellGroupData[{ Cell[8383, 274, 115, 1, 54, "Subsubsection"], Cell[CellGroupData[{ Cell[8523, 279, 283, 7, 42, "Input"], Cell[8809, 288, 173, 4, 41, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[9031, 298, 125, 1, 54, "Subsubsection"], Cell[CellGroupData[{ Cell[9181, 303, 277, 7, 42, "Input"], Cell[9461, 312, 123, 2, 41, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[9633, 320, 146, 3, 67, "Subsection"], Cell[9782, 325, 787, 22, 70, "Input"], Cell[CellGroupData[{ Cell[10594, 351, 176, 3, 42, "Input"], Cell[10773, 356, 308, 8, 60, "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[11142, 371, 250, 5, 118, "Section"], Cell[CellGroupData[{ Cell[11417, 380, 129, 1, 54, "Subsubsection"], Cell[CellGroupData[{ Cell[11571, 385, 334, 9, 42, "Input"], Cell[11908, 396, 264, 6, 41, "Output"] }, Open ]], Cell[12187, 405, 323, 9, 42, "Input"], Cell[12513, 416, 293, 8, 42, "Input"], Cell[CellGroupData[{ Cell[12831, 428, 210, 4, 42, "Input"], Cell[13044, 434, 2383, 48, 328, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15464, 487, 308, 8, 42, "Input"], Cell[15775, 497, 193, 4, 41, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[16005, 506, 371, 8, 42, "Input"], Cell[16379, 516, 96, 1, 41, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[16524, 523, 183, 2, 54, "Subsubsection"], Cell[16710, 527, 421, 11, 42, "Input"], Cell[CellGroupData[{ Cell[17156, 542, 271, 7, 42, "Input"], Cell[17430, 551, 191, 4, 41, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17658, 560, 360, 8, 42, "Input"], Cell[18021, 570, 141, 2, 41, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[18199, 577, 171, 3, 42, "Input"], Cell[18373, 582, 2339, 47, 335, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[20749, 634, 298, 6, 42, "Input"], Cell[21050, 642, 4337, 80, 539, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[25424, 727, 313, 8, 42, "Input"], Cell[25740, 737, 4209, 76, 347, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[29998, 819, 277, 5, 94, "Subsubsection"], Cell[30278, 826, 295, 8, 42, "Input"], Cell[CellGroupData[{ Cell[30598, 838, 237, 4, 42, "Input"], Cell[30838, 844, 2931, 57, 338, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[33806, 906, 263, 7, 42, "Input"], Cell[34072, 915, 161, 3, 41, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[34270, 923, 164, 3, 42, "Input"], Cell[34437, 928, 96, 1, 41, "Output"] }, Open ]], Cell[34548, 932, 395, 10, 42, "Input"], Cell[CellGroupData[{ Cell[34968, 946, 271, 7, 42, "Input"], Cell[35242, 955, 161, 3, 41, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[35440, 963, 220, 3, 42, "Input"], Cell[35663, 968, 3872, 73, 334, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[39572, 1046, 244, 5, 42, "Input"], Cell[39819, 1053, 7409, 130, 334, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[47265, 1188, 310, 8, 42, "Input"], Cell[47578, 1198, 7296, 127, 348, "Output"] }, Open ]] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)