(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.2' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 51233, 995] NotebookOptionsPosition[ 49144, 926] NotebookOutlinePosition[ 49553, 944] CellTagsIndexPosition[ 49510, 941] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["MAP30#3", "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, {3.887203586315774*^9, 3.8872035919214087`*^9}, { 3.889075926817493*^9, 3.889075926969419*^9}, {3.894353102025433*^9, 3.894353102871808*^9}}], Cell[CellGroupData[{ Cell["Question 1 \[LongDash]\[NonBreakingSpace]Type I/item censoring without \ replacement", "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, {3.8872035562635403`*^9, 3.887203571506999*^9}, { 3.889075948658783*^9, 3.889075948905105*^9}, {3.893068488938219*^9, 3.893068489604116*^9}, {3.923827128769615*^9, 3.923827131740366*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"n", "=", "24"}], ";"}], "\[IndentingNewLine]", RowBox[{ SubscriptBox["t", "0"], "=", "74000"}], "\[IndentingNewLine]", RowBox[{"data", "=", RowBox[{"{", RowBox[{ "2760.", ",", "3700.", ",", "7100.", ",", "17220.", ",", "29500.", ",", "48400.", ",", "52600.", ",", "65000."}], "}"}]}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"Length", "[", "data", "]"}]}], "\[IndentingNewLine]", RowBox[{"Total", "[", "data", "]"}], "\[IndentingNewLine]", RowBox[{"\[Tau]", "=", RowBox[{"n", "\[Times]", SubscriptBox["t", "0"]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Alpha]", "=", "0.05"}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Quantile", "[", RowBox[{ RowBox[{"ChiSquareDistribution", "[", RowBox[{"2", "*", "r"}], "]"}], ",", RowBox[{"\[Alpha]", "/", "2"}]}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Quantile", "[", RowBox[{ RowBox[{"ChiSquareDistribution", "[", RowBox[{ RowBox[{"2", "*", "r"}], "+", "2"}], "]"}], ",", RowBox[{"1", "-", RowBox[{"\[Alpha]", "/", "2"}]}]}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ SubscriptBox["\[Lambda]", "L"], "=", RowBox[{ RowBox[{"Quantile", "[", RowBox[{ RowBox[{"ChiSquareDistribution", "[", RowBox[{"2", "*", "r"}], "]"}], ",", RowBox[{"\[Alpha]", "/", "2"}]}], "]"}], "/", RowBox[{"(", RowBox[{"2", "*", "\[Tau]"}], ")"}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[Lambda]", "U"], "=", RowBox[{ RowBox[{"Quantile", "[", RowBox[{ RowBox[{"ChiSquareDistribution", "[", RowBox[{ RowBox[{"2", "*", "r"}], "+", "2"}], "]"}], ",", RowBox[{"1", "-", RowBox[{"\[Alpha]", "/", "2"}]}]}], "]"}], "/", RowBox[{"(", RowBox[{"2", "*", "\[Tau]"}], ")"}]}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "24000"}], "*", SubscriptBox["\[Lambda]", "U"]}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "24000"}], "*", SubscriptBox["\[Lambda]", "L"]}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"Using", " ", "the", " ", "tables"}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{ SubscriptBox["\[Lambda]", "L"], "=", FractionBox["6.908", RowBox[{"2", "*", "\[Tau]"}]]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[Lambda]", "U"], "=", FractionBox["31.53", RowBox[{"2", "*", "\[Tau]"}]]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "24000"}], "*", SubscriptBox["\[Lambda]", "U"]}], "]"}], "\[IndentingNewLine]", RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "24000"}], "*", SubscriptBox["\[Lambda]", "L"]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.613046442940555*^9, 3.6130464691256113`*^9}, 3.613046515822566*^9, {3.613047781331046*^9, 3.6130477819424467`*^9}, { 3.6883010211705647`*^9, 3.688301067982601*^9}, 3.688301128946279*^9, { 3.688301195796957*^9, 3.688301275846979*^9}, 3.688301330510927*^9, { 3.688301373049155*^9, 3.688301393961001*^9}, {3.688301427449625*^9, 3.68830142766224*^9}, {3.688301484550539*^9, 3.6883014896497602`*^9}, { 3.688301593301148*^9, 3.6883016208515053`*^9}, {3.68830167764058*^9, 3.688301706227622*^9}, {3.6883017374286327`*^9, 3.688301770428163*^9}, { 3.68830227393548*^9, 3.6883023804621887`*^9}, {3.6883738074743357`*^9, 3.688373849874008*^9}, {3.688374431036934*^9, 3.6883744657362328`*^9}, { 3.688374536547332*^9, 3.688374577687261*^9}, {3.688374781738389*^9, 3.6883748063008423`*^9}, {3.6885392975776587`*^9, 3.688539314502626*^9}, { 3.68853935221596*^9, 3.6885394161036453`*^9}, {3.6936488290478277`*^9, 3.693648830143045*^9}, {3.693834371896796*^9, 3.693834427154986*^9}, { 3.693834756788741*^9, 3.693834813088876*^9}, {3.6938348939538517`*^9, 3.6938348998978043`*^9}, {3.6938349343128567`*^9, 3.693834968130581*^9}, { 3.892967896767704*^9, 3.892968026651012*^9}, {3.8929682798541937`*^9, 3.892968349672009*^9}, {3.892968653025765*^9, 3.892968653376005*^9}, { 3.892968773874217*^9, 3.8929687843181458`*^9}, {3.892969924709857*^9, 3.8929700081978893`*^9}, {3.923827154554997*^9, 3.923827193679493*^9}, { 3.923827226945231*^9, 3.923827254917368*^9}, {3.9238273161563873`*^9, 3.923827368368999*^9}, {3.9238274126575947`*^9, 3.923827419505934*^9}, { 3.9238274824199657`*^9, 3.9238274857316847`*^9}, {3.9238275667328663`*^9, 3.923827572734242*^9}, {3.923827602858182*^9, 3.923827603095931*^9}, { 3.923827984137828*^9, 3.923828051887609*^9}, {3.9240947684341507`*^9, 3.924094780008293*^9}, 3.9240948141335382`*^9}], Cell[BoxData["74000"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.924094815778448*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "2760.`", ",", "3700.`", ",", "7100.`", ",", "17220.`", ",", "29500.`", ",", "48400.`", ",", "52600.`", ",", "65000.`"}], "}"}]], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.924094815780978*^9}}], Cell[BoxData["8"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.924094815782859*^9}}], Cell[BoxData["226280.`"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.924094815784706*^9}}], Cell[BoxData["1776000"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.92409481578657*^9}}], Cell[BoxData["6.907664353497003`"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.924094815788538*^9}}], Cell[BoxData["31.526378440386626`"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.9240948157904167`*^9}}], Cell[BoxData["1.944725324745778`*^-6"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.924094815792322*^9}}], Cell[BoxData["8.875669605964703`*^-6"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.924094815794326*^9}}], Cell[BoxData["0.8081431498127686`"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.924094815796217*^9}}], Cell[BoxData["0.9543990459865622`"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.924094815798161*^9}}], Cell[BoxData["1.94481981981982`*^-6"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.924094815800087*^9}}], Cell[BoxData["8.87668918918919`*^-6"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.9240948158019876`*^9}}], Cell[BoxData["0.8081233747939521`"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.9240948158038692`*^9}}], Cell[BoxData["0.9543968815248122`"], "Output", CellChangeTimes->{{3.688539413180184*^9, 3.688539431517209*^9}, 3.693834428357483*^9, 3.6938348143894033`*^9, 3.69383490064172*^9, { 3.693834956013781*^9, 3.693834968811304*^9}, 3.892968314408503*^9, 3.892968350293096*^9, 3.892968653962126*^9, 3.892968799385178*^9, 3.892969953676853*^9, {3.892970001694558*^9, 3.892970010536208*^9}, 3.9238273696441097`*^9, 3.923827420862028*^9, 3.923827487097124*^9, { 3.923827573608391*^9, 3.923827603534046*^9}, 3.9238280030893097`*^9, 3.923828053649527*^9, {3.924094786104199*^9, 3.924094815805784*^9}}] }, Open ]] }, Open ]], Cell["Question 2", "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, {3.8872035562635403`*^9, 3.887203571506999*^9}, { 3.889075948658783*^9, 3.889075948905105*^9}, {3.889233499580864*^9, 3.889233499742189*^9}, {3.893051552889963*^9, 3.893051553359744*^9}, { 3.893068465963595*^9, 3.893068480337051*^9}, {3.893068535343358*^9, 3.893068536877803*^9}, {3.923841967755245*^9, 3.923841967842307*^9}}], Cell[CellGroupData[{ Cell["Exerc\[IAcute]cio 5(b)", "Subsection", CellChangeTimes->{{3.528544419253316*^9, 3.528544422002598*^9}, { 3.5285533563574753`*^9, 3.528553367972056*^9}, {3.528553593741721*^9, 3.5285535972847424`*^9}, {3.5293340763983088`*^9, 3.529334084946261*^9}, { 3.579441979545072*^9, 3.579442000295053*^9}, {3.579510984491907*^9, 3.579510996199205*^9}, {3.709138188940858*^9, 3.7091381889906693`*^9}, { 3.709203622201426*^9, 3.7092036225762863`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ SubscriptBox["p", "0"], "=", "0.001"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Alpha]", "=", "0.005"}], ";"}], "\[IndentingNewLine]", RowBox[{"LCLalpha", "=", FractionBox[ RowBox[{"Log", "[", RowBox[{"1", "-", RowBox[{"\[Alpha]", "/", "2"}]}], "]"}], RowBox[{"Log", "[", RowBox[{"1", "-", SubscriptBox["p", "0"]}], "]"}]]}], "\[IndentingNewLine]", RowBox[{"UCLalpha", "=", FractionBox[ RowBox[{"Log", "[", RowBox[{"\[Alpha]", "/", "2"}], "]"}], RowBox[{"Log", "[", RowBox[{"1", "-", SubscriptBox["p", "0"]}], "]"}]]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ARLalpha", "[", "\[Rho]_", "]"}], "=", RowBox[{"1", "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"(", RowBox[{ RowBox[{"CDF", "[", RowBox[{ RowBox[{"GeometricDistribution", "[", RowBox[{"\[Rho]", "*", SubscriptBox["p", "0"]}], "]"}], ",", RowBox[{"Floor", "[", "UCLalpha", "]"}]}], "]"}], "-", RowBox[{"CDF", "[", RowBox[{ RowBox[{"GeometricDistribution", "[", RowBox[{"\[Rho]", "*", SubscriptBox["p", "0"]}], "]"}], ",", RowBox[{ RowBox[{"Ceiling", "[", RowBox[{"Max", "[", RowBox[{"0", ",", "LCLalpha"}], "]"}], "]"}], "-", "1"}]}], "]"}]}], ")"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Round", "[", RowBox[{ RowBox[{"ARLalpha", "[", "1", "]"}], ",", "0.001"}], "]"}], "\[IndentingNewLine]", RowBox[{"Round", "[", RowBox[{ RowBox[{"ARLalpha", "[", "1.1", "]"}], ",", "0.001"}], "]"}]}], "Input", CellChangeTimes->{{3.530878749737143*^9, 3.530878825489481*^9}, { 3.642811660861704*^9, 3.6428118472259192`*^9}, {3.642811883095519*^9, 3.6428119142064905`*^9}, {3.642812002257884*^9, 3.6428120138209763`*^9}, { 3.642812073080366*^9, 3.6428120884249263`*^9}, 3.64281264084134*^9, { 3.6439511864210434`*^9, 3.643951659606876*^9}, {3.6439517161748266`*^9, 3.643951721815753*^9}, {3.6439569034050674`*^9, 3.6439570215136776`*^9}, { 3.6439571015556216`*^9, 3.6439571021806507`*^9}, {3.6439578368419905`*^9, 3.6439579586772885`*^9}, {3.64398806330055*^9, 3.6439880636755676`*^9}, { 3.643988961316739*^9, 3.6439889619417963`*^9}, {3.6439891514628034`*^9, 3.6439891517596865`*^9}, {3.6439900435563836`*^9, 3.6439900439783115`*^9}, {3.6440389042129636`*^9, 3.644038919127938*^9}, { 3.6482143630019493`*^9, 3.6482147757387495`*^9}, {3.6482148611768475`*^9, 3.648214868416686*^9}, {3.6482149771171265`*^9, 3.648214983130145*^9}, { 3.648215175168145*^9, 3.6482151836217055`*^9}, 3.648216928072667*^9, { 3.6482184514026318`*^9, 3.6482184762789493`*^9}, 3.6482187418242617`*^9, { 3.64821955916788*^9, 3.648219559292887*^9}, {3.6482196932374797`*^9, 3.648219702019167*^9}, {3.6482199509073453`*^9, 3.648219959220315*^9}, { 3.648396016382806*^9, 3.6483960165859413`*^9}, {3.6483962068177233`*^9, 3.6483962415539465`*^9}, {3.648396418126549*^9, 3.6483964335023966`*^9}, { 3.648396610847905*^9, 3.6483969182567453`*^9}, {3.6483969826820345`*^9, 3.6483970034410973`*^9}, {3.6483970513342576`*^9, 3.6483971262404065`*^9}, {3.648397170899021*^9, 3.6483972240790095`*^9}, { 3.648398056508874*^9, 3.6483980692908344`*^9}, 3.64839873483854*^9, { 3.6483987815129223`*^9, 3.648398816686634*^9}, {3.6483991553383427`*^9, 3.6483991884494696`*^9}, {3.648399230795458*^9, 3.6483992352956963`*^9}, { 3.6483994738653345`*^9, 3.6483994898627357`*^9}, {3.6483995861600275`*^9, 3.648399605145415*^9}, {3.64839964156921*^9, 3.648399670840459*^9}, { 3.6483997581419563`*^9, 3.6483998807757993`*^9}, {3.648400525523752*^9, 3.64840060916391*^9}, {3.6484330822985497`*^9, 3.6484331027683516`*^9}, { 3.648433134926222*^9, 3.6484331654746637`*^9}, {3.6484332526891108`*^9, 3.6484332656272755`*^9}, {3.648434983320963*^9, 3.6484350545121207`*^9}, { 3.6484351089367857`*^9, 3.6484351958576*^9}, {3.648435357681711*^9, 3.648435382562972*^9}, {3.6484354529009438`*^9, 3.6484354725738006`*^9}, { 3.6484355314674478`*^9, 3.6484355435305667`*^9}, {3.6484356222057934`*^9, 3.648435622565189*^9}, {3.648435660129614*^9, 3.6484356786060233`*^9}, { 3.648440481756686*^9, 3.648440502585909*^9}, {3.648440668969446*^9, 3.648440739191799*^9}, {3.6484427691719894`*^9, 3.6484430496863832`*^9}, 3.648443563666012*^9, {3.648523810906583*^9, 3.6485238121566515`*^9}, { 3.648523855580759*^9, 3.64852411101979*^9}, {3.6485241855079827`*^9, 3.6485242967930017`*^9}, {3.6485243351043005`*^9, 3.6485243371512747`*^9}, {3.6485245379868903`*^9, 3.648524601357813*^9}, { 3.6485248493950157`*^9, 3.6485249159609313`*^9}, {3.6485254799604125`*^9, 3.6485254993900895`*^9}, 3.648531203725416*^9, {3.651046109236498*^9, 3.6510461403162236`*^9}, {3.6510461912407403`*^9, 3.651046330703884*^9}, { 3.6510464205739737`*^9, 3.651046500801657*^9}, {3.6510465367722735`*^9, 3.651046570617801*^9}, {3.651046699785194*^9, 3.651046712707737*^9}, { 3.651046820417066*^9, 3.6510468260111055`*^9}, {3.651046862903633*^9, 3.651046894170885*^9}, {3.651047053935693*^9, 3.651047062032995*^9}, { 3.6510470926439543`*^9, 3.651047096081625*^9}, {3.651047134474236*^9, 3.651047250731969*^9}, {3.6510472891089635`*^9, 3.6510474014180665`*^9}, { 3.6510474380817213`*^9, 3.6510474629039793`*^9}, {3.6510475208132167`*^9, 3.6510475407829995`*^9}, {3.6510482353963995`*^9, 3.6510483374797945`*^9}, {3.651048386250037*^9, 3.6510483970318394`*^9}, { 3.651049441928537*^9, 3.6510494921498933`*^9}, {3.6510495279798627`*^9, 3.6510495315738325`*^9}, {3.6510497761977406`*^9, 3.6510498278549256`*^9}, {3.6510498739041824`*^9, 3.6510499221254253`*^9}, {3.651049956970978*^9, 3.651049973311988*^9}, { 3.6510500129546647`*^9, 3.6510500349870863`*^9}, {3.651050077426755*^9, 3.6510501182144675`*^9}, 3.651050151075576*^9, {3.651051176310915*^9, 3.651051199855386*^9}, {3.6510512374667053`*^9, 3.651051289156886*^9}, { 3.651068684642606*^9, 3.651068768452506*^9}, {3.651068808985833*^9, 3.651068914460059*^9}, {3.65106896801672*^9, 3.6510690618184223`*^9}, { 3.6510691881021214`*^9, 3.6510692500428047`*^9}, {3.6510693026705513`*^9, 3.6510693118379436`*^9}, {3.651069407090214*^9, 3.6510694421857667`*^9}, 3.6510695755768337`*^9, {3.6510696572529325`*^9, 3.6510696863169374`*^9}, { 3.651069810377825*^9, 3.6510698390980597`*^9}, {3.651070057412033*^9, 3.6510700575370097`*^9}, {3.6510702838258657`*^9, 3.6510703333596773`*^9}, {3.6510703746117873`*^9, 3.651070375002428*^9}, { 3.6510704082853975`*^9, 3.6510704128950415`*^9}, {3.6510704605332165`*^9, 3.651070480050564*^9}, {3.6510705244591117`*^9, 3.6510705705396194`*^9}, { 3.6510706107448244`*^9, 3.6510706139637423`*^9}, 3.651073577889188*^9, { 3.651073873425028*^9, 3.651073875956383*^9}, {3.6510740375669575`*^9, 3.651074063365163*^9}, {3.6510743040767803`*^9, 3.6510743275623693`*^9}, { 3.6510744283644595`*^9, 3.651074486952817*^9}, {3.6511110331843395`*^9, 3.651111047044438*^9}, {3.651111081405588*^9, 3.6511110838275948`*^9}, { 3.6511111558194313`*^9, 3.651111277723941*^9}, {3.6511114164401116`*^9, 3.6511114833243656`*^9}, {3.651111525420294*^9, 3.651111575409565*^9}, { 3.651111762068589*^9, 3.651111776647473*^9}, 3.6511120236444855`*^9, { 3.651112068712923*^9, 3.651112104894275*^9}, {3.6511121507091494`*^9, 3.6511121946476917`*^9}, {3.6511122383999567`*^9, 3.651112324953232*^9}, { 3.6511123860684695`*^9, 3.651112394725133*^9}, 3.6511134828663054`*^9, 3.6511138490366907`*^9, {3.6511139848217545`*^9, 3.6511140495594716`*^9}, { 3.651114120439475*^9, 3.6511141897012367`*^9}, {3.651114242953992*^9, 3.651114249657463*^9}, {3.6511144377653017`*^9, 3.651114455844368*^9}, { 3.651114570037122*^9, 3.6511145886943436`*^9}, {3.651114722428753*^9, 3.6511148364137945`*^9}, {3.651114938195285*^9, 3.651114956843413*^9}, 3.651115036706913*^9, {3.6512457868882217`*^9, 3.6512457937010746`*^9}, { 3.6512459521307535`*^9, 3.651246057480318*^9}, {3.651246138375127*^9, 3.6512462763577185`*^9}, 3.6512466250840893`*^9, {3.651247411611371*^9, 3.6512474294091663`*^9}, {3.6512474877624903`*^9, 3.651247489559458*^9}, { 3.651247617262752*^9, 3.651247618669073*^9}, {3.6512481750994377`*^9, 3.651248176724526*^9}, {3.651248264994712*^9, 3.651248289824136*^9}, 3.6512483488846483`*^9, {3.651248400215392*^9, 3.6512484467646837`*^9}, { 3.6512485210361586`*^9, 3.6512485212861724`*^9}, {3.651249529975602*^9, 3.651249530491252*^9}, 3.6519817188008456`*^9, {3.6519827283016586`*^9, 3.651982729553496*^9}, {3.6519829131255445`*^9, 3.651982957369852*^9}, { 3.65198298860769*^9, 3.6519830299802895`*^9}, {3.6519832467862835`*^9, 3.651983348618451*^9}, 3.651983380158491*^9, {3.651983415661169*^9, 3.651983446182529*^9}, {3.651983524511775*^9, 3.6519835699607296`*^9}, { 3.6519836478636928`*^9, 3.651983675916567*^9}, {3.6519853122313733`*^9, 3.6519853127626524`*^9}, {3.6519853614057937`*^9, 3.6519853833912983`*^9}, 3.651985422283944*^9, {3.6519856468479414`*^9, 3.651985647051077*^9}, { 3.6519870888653183`*^9, 3.651987103631705*^9}, {3.6519872257724037`*^9, 3.651987250976839*^9}, {3.652014127930235*^9, 3.6520142283838716`*^9}, 3.6520142954686203`*^9, 3.65201440712531*^9, {3.6520144587025275`*^9, 3.6520145394163637`*^9}, {3.652015204416233*^9, 3.6520152050896807`*^9}, { 3.652015375663684*^9, 3.65201537832546*^9}, {3.652015467311776*^9, 3.652015476304781*^9}, {3.6520155347308755`*^9, 3.652015535462364*^9}, { 3.652021723200083*^9, 3.652021759826982*^9}, {3.652021880432046*^9, 3.652021916043269*^9}, {3.6520219605299387`*^9, 3.6520219930003757`*^9}, { 3.652022139377465*^9, 3.652022139533716*^9}, {3.6520221817859087`*^9, 3.652022181942159*^9}, {3.6520222847776356`*^9, 3.6520222849807773`*^9}, { 3.6520223345145893`*^9, 3.652022334639597*^9}, {3.6520758537520247`*^9, 3.652076020329414*^9}, {3.652076102979069*^9, 3.65207610353344*^9}, { 3.6520761803186617`*^9, 3.652076238861906*^9}, {3.6520762803305683`*^9, 3.652076374803684*^9}, {3.652076411931451*^9, 3.6520765308292923`*^9}, { 3.65207656566553*^9, 3.6520765853316545`*^9}, {3.6520767099412785`*^9, 3.652076742677117*^9}, {3.652076823269023*^9, 3.652076833579904*^9}, { 3.6520768782118893`*^9, 3.6520769682459517`*^9}, {3.652077223729417*^9, 3.6520772421757193`*^9}, {3.652077285250411*^9, 3.6520772853644867`*^9}, { 3.6520775150549517`*^9, 3.652077524495246*^9}, {3.652077878388754*^9, 3.652077947398785*^9}, {3.6520779965911226`*^9, 3.652078028192195*^9}, { 3.652078085260262*^9, 3.652078116677724*^9}, {3.6520781911894245`*^9, 3.6520781990406656`*^9}, {3.652078244159725*^9, 3.6520782461860714`*^9}, 3.65207835347007*^9, {3.652078437920399*^9, 3.6520784967217035`*^9}, { 3.652079126830454*^9, 3.652079135310108*^9}, {3.6520836920638533`*^9, 3.652083730523508*^9}, {3.6520837739404755`*^9, 3.652083841778464*^9}, { 3.6520838750476646`*^9, 3.6520839150028725`*^9}, {3.6520839470312433`*^9, 3.6520839705069*^9}, {3.652084108395259*^9, 3.652084127860237*^9}, { 3.6520841925836244`*^9, 3.6520842289538813`*^9}, {3.65208430978146*^9, 3.652084333536306*^9}, {3.652084548597744*^9, 3.6520845634816675`*^9}, { 3.652084665789527*^9, 3.652084677409282*^9}, {3.6520849280879498`*^9, 3.652084940209035*^9}, {3.6520851457627597`*^9, 3.652085213563983*^9}, { 3.6525901998857646`*^9, 3.65259020005765*^9}, {3.652590239419057*^9, 3.6525902489195423`*^9}, {3.652591453923854*^9, 3.6525914540644846`*^9}, { 3.652591615476457*^9, 3.652591660681926*^9}, {3.6525917272369947`*^9, 3.652591738925105*^9}, {3.652591820679332*^9, 3.6525918436492653`*^9}, { 3.652592063688792*^9, 3.6525921233793783`*^9}, {3.652592318016054*^9, 3.6525923600807333`*^9}, {3.65259252233619*^9, 3.652592523633133*^9}, { 3.652592732694411*^9, 3.652592947914591*^9}, {3.6525929784786654`*^9, 3.652592992534289*^9}, 3.6525930612409678`*^9, {3.652593157417141*^9, 3.652593168167697*^9}, {3.652593375675105*^9, 3.652593444457201*^9}, { 3.652593481240349*^9, 3.652593552111876*^9}, {3.652593592613968*^9, 3.6525936145838566`*^9}, 3.652593678107877*^9, 3.652593749564661*^9, { 3.65259433686981*^9, 3.6525943580115213`*^9}, {3.6528846789747877`*^9, 3.6528846966026993`*^9}, {3.6528847738606205`*^9, 3.65288480434057*^9}, 3.652885021149158*^9, 3.652885051956048*^9, {3.6528851078318744`*^9, 3.65288511123977*^9}, {3.652885143875708*^9, 3.652885175912739*^9}, { 3.6528853608913603`*^9, 3.652885391254921*^9}, {3.65288557997744*^9, 3.652885672817745*^9}, {3.6528857575843534`*^9, 3.6528857645881767`*^9}, { 3.6528858627422237`*^9, 3.652885872733899*^9}, {3.652885919863056*^9, 3.6528859771331267`*^9}, {3.6528860192637224`*^9, 3.6528860422899337`*^9}, {3.6528860737671824`*^9, 3.6528860834646864`*^9}, {3.652886161463393*^9, 3.652886172753705*^9}, { 3.6528862132247553`*^9, 3.6528862804694386`*^9}, {3.6528863415386295`*^9, 3.652886348042511*^9}, {3.6528864232892666`*^9, 3.652886456331921*^9}, { 3.6529328610826488`*^9, 3.652932881166094*^9}, {3.6529329245400267`*^9, 3.6529329279443007`*^9}, {3.6529337989931765`*^9, 3.652933889595605*^9}, { 3.652934104170932*^9, 3.6529341547586775`*^9}, {3.652934202377386*^9, 3.6529342047219563`*^9}, {3.652934246569869*^9, 3.6529342513420477`*^9}, { 3.6569136382328243`*^9, 3.656913690105299*^9}, {3.6569138792420125`*^9, 3.656914051099386*^9}, {3.6569141136960735`*^9, 3.656914282204347*^9}, { 3.6569144001868477`*^9, 3.6569144114233303`*^9}, {3.656917849168333*^9, 3.6569178720262527`*^9}, {3.6569179084435806`*^9, 3.6569179741848593`*^9}, {3.6569180442040043`*^9, 3.6569180586608953`*^9}, {3.6571025303468328`*^9, 3.657102583750871*^9}, { 3.657102630933796*^9, 3.6571027063630095`*^9}, {3.6571031854964876`*^9, 3.6571032403597584`*^9}, {3.657103282836608*^9, 3.657103326469346*^9}, 3.6571034111824083`*^9, {3.657104244502985*^9, 3.6571042884377604`*^9}, { 3.6571043974941473`*^9, 3.657104433276503*^9}, {3.6571073867872877`*^9, 3.657107447667839*^9}, {3.657108501403778*^9, 3.6571085682743874`*^9}, { 3.657135736726464*^9, 3.657135756001042*^9}, {3.6571358061294594`*^9, 3.657135833511513*^9}, {3.6571359764311285`*^9, 3.6571359793687572`*^9}, { 3.657136033172112*^9, 3.657136064205645*^9}, {3.657136210325037*^9, 3.6571362673353977`*^9}, {3.6571363101100245`*^9, 3.657136323473075*^9}, { 3.657136374180547*^9, 3.657136440739746*^9}, {3.657136475289093*^9, 3.657136526527296*^9}, {3.657136582647125*^9, 3.6571365836940603`*^9}, { 3.657136807036928*^9, 3.657136837469445*^9}, {3.658572102633685*^9, 3.658572131166413*^9}, 3.662367371809029*^9, {3.662367403295029*^9, 3.6623674038106833`*^9}, {3.662370084168029*^9, 3.662370126549384*^9}, { 3.6623703089732227`*^9, 3.662370316395492*^9}, {3.664889129367372*^9, 3.6648891296472*^9}, {3.664892750093503*^9, 3.664892781879636*^9}, { 3.664956184539263*^9, 3.664956329518168*^9}, {3.664956383485647*^9, 3.6649564205571404`*^9}, {3.664956689844364*^9, 3.664956756293812*^9}, 3.664956792863696*^9, {3.664956881319983*^9, 3.6649568815041018`*^9}, { 3.665602174064036*^9, 3.6656021773674297`*^9}, {3.709199363240451*^9, 3.709199475645117*^9}, {3.709199577620315*^9, 3.709199683948284*^9}, { 3.709199716560068*^9, 3.709199858178084*^9}, {3.709199940575366*^9, 3.7091999445563107`*^9}, {3.709200152703054*^9, 3.7092001788259697`*^9}, { 3.7092005473361483`*^9, 3.70920056125877*^9}, {3.709201376647849*^9, 3.70920138943381*^9}, {3.7092017944423447`*^9, 3.709201813729298*^9}, { 3.709201937073657*^9, 3.709201938410056*^9}, 3.7092036070165157`*^9, 3.923842142532701*^9}], Cell[BoxData["2.5018784443108673`"], "Output", CellChangeTimes->{ 3.709199678936953*^9, {3.7091997175818377`*^9, 3.709199799484167*^9}, { 3.7091998526900043`*^9, 3.709199859055732*^9}, 3.709199945271912*^9, { 3.7092001536930304`*^9, 3.709200179609703*^9}, 3.70920056170963*^9, 3.709201390300681*^9, 3.7092018144536343`*^9, 3.709201946545998*^9, 3.709202306704199*^9, 3.709203607590664*^9, 3.709203656869985*^9, 3.709437867212447*^9, 3.709447791975286*^9, 3.923842002905366*^9, 3.92384214586662*^9, 3.924094821398622*^9, 3.924097296120173*^9, 3.924097329184902*^9}], Cell[BoxData["5988.468315295908`"], "Output", CellChangeTimes->{ 3.709199678936953*^9, {3.7091997175818377`*^9, 3.709199799484167*^9}, { 3.7091998526900043`*^9, 3.709199859055732*^9}, 3.709199945271912*^9, { 3.7092001536930304`*^9, 3.709200179609703*^9}, 3.70920056170963*^9, 3.709201390300681*^9, 3.7092018144536343`*^9, 3.709201946545998*^9, 3.709202306704199*^9, 3.709203607590664*^9, 3.709203656869985*^9, 3.709437867212447*^9, 3.709447791975286*^9, 3.923842002905366*^9, 3.92384214586662*^9, 3.924094821398622*^9, 3.924097296120173*^9, 3.924097329187386*^9}], Cell[BoxData["181.961`"], "Output", CellChangeTimes->{ 3.709199678936953*^9, {3.7091997175818377`*^9, 3.709199799484167*^9}, { 3.7091998526900043`*^9, 3.709199859055732*^9}, 3.709199945271912*^9, { 3.7092001536930304`*^9, 3.709200179609703*^9}, 3.70920056170963*^9, 3.709201390300681*^9, 3.7092018144536343`*^9, 3.709201946545998*^9, 3.709202306704199*^9, 3.709203607590664*^9, 3.709203656869985*^9, 3.709437867212447*^9, 3.709447791975286*^9, 3.923842002905366*^9, 3.92384214586662*^9, 3.924094821398622*^9, 3.924097296120173*^9, 3.92409732918921*^9}], Cell[BoxData["214.21`"], "Output", CellChangeTimes->{ 3.709199678936953*^9, {3.7091997175818377`*^9, 3.709199799484167*^9}, { 3.7091998526900043`*^9, 3.709199859055732*^9}, 3.709199945271912*^9, { 3.7092001536930304`*^9, 3.709200179609703*^9}, 3.70920056170963*^9, 3.709201390300681*^9, 3.7092018144536343`*^9, 3.709201946545998*^9, 3.709202306704199*^9, 3.709203607590664*^9, 3.709203656869985*^9, 3.709437867212447*^9, 3.709447791975286*^9, 3.923842002905366*^9, 3.92384214586662*^9, 3.924094821398622*^9, 3.924097296120173*^9, 3.924097329191022*^9}] }, Open ]], Cell[CellGroupData[{ Cell["Question 3", "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, {3.8872035562635403`*^9, 3.887203571506999*^9}, { 3.889075948658783*^9, 3.889075948905105*^9}, {3.889233499580864*^9, 3.889233499742189*^9}, {3.893051552889963*^9, 3.893051553359744*^9}, { 3.893068465963595*^9, 3.893068480337051*^9}, {3.893068535343358*^9, 3.893068536877803*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"n", "=", "9"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[Mu]", "0"], "=", "350."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[Sigma]", "0"], "=", "2."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Alpha]", "=", RowBox[{"1", "/", "370.4"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"distmu", "=", RowBox[{"NormalDistribution", "[", RowBox[{"0", ",", "1"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Gamma]mu", "=", RowBox[{"Quantile", "[", RowBox[{"distmu", ",", RowBox[{"1", "-", FractionBox["\[Alpha]", "2"]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Gamma]mu", "=", "3."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Xi]mu", "[", RowBox[{"\[Delta]_", ",", "\[Theta]_"}], "]"}], "=", RowBox[{"1", "-", RowBox[{"(", RowBox[{ RowBox[{"CDF", "[", RowBox[{"distmu", ",", FractionBox[ RowBox[{"\[Gamma]mu", "-", "\[Delta]"}], "\[Theta]"]}], "]"}], "-", RowBox[{"CDF", "[", RowBox[{"distmu", ",", FractionBox[ RowBox[{ RowBox[{"-", "\[Gamma]mu"}], "-", "\[Delta]"}], "\[Theta]"]}], "]"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"\[Xi]mu", "[", RowBox[{"0", ",", "1"}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ARLmu", "[", RowBox[{"\[Delta]_", ",", "\[Theta]_"}], "]"}], "=", FractionBox["1", RowBox[{"\[Xi]mu", "[", RowBox[{"\[Delta]", ",", "\[Theta]"}], "]"}]]}], ";"}], "\[IndentingNewLine]", RowBox[{"ARLmu", "[", RowBox[{"0", ",", "1"}], "]"}]}], "Input", CellChangeTimes->{{3.7094504679764843`*^9, 3.709450468716999*^9}, 3.7094683674381323`*^9, {3.709468888133259*^9, 3.709468897573944*^9}, { 3.7095194337903423`*^9, 3.7095194484756308`*^9}, {3.7095195622078333`*^9, 3.709519586103156*^9}, 3.70987341051127*^9, 3.923844268950798*^9}], Cell[BoxData["0.002699796063260096`"], "Output", CellChangeTimes->{{3.709450458270104*^9, 3.7094504695446177`*^9}, 3.709467075671455*^9, 3.709468757516506*^9, {3.7094688822001677`*^9, 3.709468889274807*^9}, 3.7094689411682158`*^9, 3.709486303760414*^9, 3.709488197689188*^9, {3.709519445002728*^9, 3.709519448957028*^9}, { 3.7095195687356787`*^9, 3.709519604711627*^9}, 3.709531399278706*^9, 3.709873411458674*^9, 3.709873898247423*^9, 3.923843749204625*^9, 3.923844288174704*^9, 3.9240948251224813`*^9}], Cell[BoxData["370.3983473449716`"], "Output", CellChangeTimes->{{3.709450458270104*^9, 3.7094504695446177`*^9}, 3.709467075671455*^9, 3.709468757516506*^9, {3.7094688822001677`*^9, 3.709468889274807*^9}, 3.7094689411682158`*^9, 3.709486303760414*^9, 3.709488197689188*^9, {3.709519445002728*^9, 3.709519448957028*^9}, { 3.7095195687356787`*^9, 3.709519604711627*^9}, 3.709531399278706*^9, 3.709873411458674*^9, 3.709873898247423*^9, 3.923843749204625*^9, 3.923844288174704*^9, 3.924094825124991*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"n", "=", "9"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[Mu]", "0"], "=", "350."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[Sigma]", "0"], "=", "2."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Alpha]", "=", RowBox[{"1", "/", "370.4"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"distsigma", "=", RowBox[{"ChiSquareDistribution", "[", RowBox[{"n", "-", "1"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"\[Gamma]sigma", " ", "=", RowBox[{"Round", "[", RowBox[{ RowBox[{"Quantile", "[", RowBox[{"distsigma", ",", RowBox[{"1", "-", "\[Alpha]"}]}], "]"}], ",", "0.000001"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Xi]sigma", "[", "\[Theta]_", "]"}], "=", RowBox[{"1", "-", RowBox[{"CDF", "[", RowBox[{"distsigma", ",", FractionBox["\[Gamma]sigma", SuperscriptBox["\[Theta]", "2"]]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Xi]sigma", "[", "1", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ARLsigma", "[", "\[Theta]_", "]"}], "=", FractionBox["1", RowBox[{"\[Xi]sigma", "[", "\[Theta]", "]"}]]}], ";"}], "\[IndentingNewLine]", RowBox[{"ARLsigma", "[", "1", "]"}]}], "Input", CellChangeTimes->{{3.610566851562529*^9, 3.610567236912198*^9}, { 3.6105676861101637`*^9, 3.610567688877533*^9}, {3.610600911285817*^9, 3.610600960216777*^9}, {3.610600991170627*^9, 3.6106010412172527`*^9}, { 3.610704762320983*^9, 3.610704762583201*^9}, {3.629216315522439*^9, 3.629216452138616*^9}, {3.629217432516494*^9, 3.62921745745497*^9}, { 3.6292177033925047`*^9, 3.629217735654768*^9}, 3.629217773089197*^9, { 3.6292643556015053`*^9, 3.6292643705074463`*^9}, {3.629269564739069*^9, 3.629269577276051*^9}, {3.6293408145163107`*^9, 3.62934081809447*^9}, { 3.629340849614993*^9, 3.629340899714168*^9}, {3.6293410738113337`*^9, 3.6293411054385777`*^9}, 3.6293418132986794`*^9, {3.629344670455871*^9, 3.6293446963241377`*^9}, {3.69181686049205*^9, 3.691817269191139*^9}, { 3.6918173152889547`*^9, 3.6918173772397957`*^9}, {3.691817756229415*^9, 3.6918177609950523`*^9}, {3.691818934978718*^9, 3.6918189662325373`*^9}, { 3.691819857216969*^9, 3.6918199536372137`*^9}, {3.709450344610984*^9, 3.709450478876845*^9}, {3.709450521435423*^9, 3.709450551950953*^9}, { 3.70946719882867*^9, 3.709467248109158*^9}, {3.7094682883406687`*^9, 3.709468376669092*^9}, {3.709468902442704*^9, 3.7094689320188837`*^9}, { 3.709468966583271*^9, 3.709468968405727*^9}, {3.70948824414428*^9, 3.709488245910491*^9}, {3.709519483851852*^9, 3.709519492040966*^9}}], Cell[BoxData["23.574603`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.709450530573125*^9, 3.709467079307357*^9, {3.709467214010242*^9, 3.709467248876602*^9}, {3.7094683102500134`*^9, 3.7094683461978197`*^9}, 3.7094683783955193`*^9, 3.709468893480982*^9, {3.709468926935431*^9, 3.709468932530308*^9}, 3.709468969244226*^9, 3.7094863058171864`*^9, { 3.7094881995547*^9, 3.709488211171139*^9}, 3.709488246566983*^9, 3.709519492659822*^9, {3.709519571310405*^9, 3.709519606254333*^9}, 3.70953140121201*^9, 3.7098734139581842`*^9, 3.709873899561524*^9, 3.9238437517180843`*^9, 3.923844289199457*^9, 3.9240948288427067`*^9}], Cell[BoxData["370.4000518683244`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.709450530573125*^9, 3.709467079307357*^9, {3.709467214010242*^9, 3.709467248876602*^9}, {3.7094683102500134`*^9, 3.7094683461978197`*^9}, 3.7094683783955193`*^9, 3.709468893480982*^9, {3.709468926935431*^9, 3.709468932530308*^9}, 3.709468969244226*^9, 3.7094863058171864`*^9, { 3.7094881995547*^9, 3.709488211171139*^9}, 3.709488246566983*^9, 3.709519492659822*^9, {3.709519571310405*^9, 3.709519606254333*^9}, 3.70953140121201*^9, 3.7098734139581842`*^9, 3.709873899561524*^9, 3.9238437517180843`*^9, 3.923844289199457*^9, 3.924094828845353*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"shiftmu", "=", "0.25"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"shiftsigma", "=", SqrtBox[ FractionBox["23.574603", "21.95"]]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Round", "[", RowBox[{ RowBox[{"\[Xi]mu", "[", RowBox[{"shiftmu", ",", "shiftsigma"}], "]"}], ",", "0.000001"}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Round", "[", RowBox[{ RowBox[{"\[Xi]sigma", "[", "shiftsigma", "]"}], ",", "0.000001"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Round", "[", RowBox[{ RowBox[{"0.004839", "+", "0.005009", "-", RowBox[{"0.004839", "*", "0.005009"}]}], ",", "0.000001"}], "]"}], "\[IndentingNewLine]", RowBox[{"1", "-", RowBox[{"CDF", "[", RowBox[{ RowBox[{"BinomialDistribution", "[", RowBox[{"10", ",", "%"}], "]"}], ",", "1"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"Round", "[", RowBox[{ RowBox[{"1", "-", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "0.009824"}], ")"}], "10"], "-", RowBox[{"10", "*", " ", "0.009824", "*", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "0.009824"}], ")"}], "9"]}]}], ",", "0.000001"}], "]"}]}], "Input", CellChangeTimes->{{3.709519504066094*^9, 3.7095195472890673`*^9}, { 3.709519608933465*^9, 3.7095196209071207`*^9}, 3.7095315195321493`*^9, 3.7095315674508944`*^9, {3.92384381980895*^9, 3.9238438683333063`*^9}, { 3.92384393495964*^9, 3.923844001123456*^9}, {3.923844193663289*^9, 3.923844197125134*^9}, {3.923844278500531*^9, 3.923844279674679*^9}}], Cell[BoxData["0.0048389999999999996`"], "Output", CellChangeTimes->{{3.7095195504706984`*^9, 3.70951962248741*^9}, 3.709531403861274*^9, 3.7095315200521603`*^9, 3.709531567927342*^9, 3.709873417009438*^9, 3.709873902066115*^9, 3.9238437759800577`*^9, 3.923843826268552*^9, 3.923843869293729*^9, {3.9238439649231253`*^9, 3.923844002281774*^9}, 3.923844210500799*^9, {3.923844284483345*^9, 3.9238442904525337`*^9}, 3.924094840663309*^9}], Cell[BoxData["0.0050089999999999996`"], "Output", CellChangeTimes->{{3.7095195504706984`*^9, 3.70951962248741*^9}, 3.709531403861274*^9, 3.7095315200521603`*^9, 3.709531567927342*^9, 3.709873417009438*^9, 3.709873902066115*^9, 3.9238437759800577`*^9, 3.923843826268552*^9, 3.923843869293729*^9, {3.9238439649231253`*^9, 3.923844002281774*^9}, 3.923844210500799*^9, {3.923844284483345*^9, 3.9238442904525337`*^9}, 3.9240948406649303`*^9}], Cell[BoxData["0.009824`"], "Output", CellChangeTimes->{{3.7095195504706984`*^9, 3.70951962248741*^9}, 3.709531403861274*^9, 3.7095315200521603`*^9, 3.709531567927342*^9, 3.709873417009438*^9, 3.709873902066115*^9, 3.9238437759800577`*^9, 3.923843826268552*^9, 3.923843869293729*^9, {3.9238439649231253`*^9, 3.923844002281774*^9}, 3.923844210500799*^9, {3.923844284483345*^9, 3.9238442904525337`*^9}, 3.924094840665958*^9}], Cell[BoxData["0.004121220954537597`"], "Output", CellChangeTimes->{{3.7095195504706984`*^9, 3.70951962248741*^9}, 3.709531403861274*^9, 3.7095315200521603`*^9, 3.709531567927342*^9, 3.709873417009438*^9, 3.709873902066115*^9, 3.9238437759800577`*^9, 3.923843826268552*^9, 3.923843869293729*^9, {3.9238439649231253`*^9, 3.923844002281774*^9}, 3.923844210500799*^9, {3.923844284483345*^9, 3.9238442904525337`*^9}, 3.9240948406754436`*^9}], Cell[BoxData["0.004121`"], "Output", CellChangeTimes->{{3.7095195504706984`*^9, 3.70951962248741*^9}, 3.709531403861274*^9, 3.7095315200521603`*^9, 3.709531567927342*^9, 3.709873417009438*^9, 3.709873902066115*^9, 3.9238437759800577`*^9, 3.923843826268552*^9, 3.923843869293729*^9, {3.9238439649231253`*^9, 3.923844002281774*^9}, 3.923844210500799*^9, {3.923844284483345*^9, 3.9238442904525337`*^9}, 3.9240948406767063`*^9}] }, Open ]] }, Open ]] }, Open ]] }, WindowSize->{652, 1256}, WindowMargins->{{Automatic, 111}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, FrontEndVersion->"10.2 for Mac OS X x86 (32-bit, 64-bit Kernel) (July 29, \ 2015)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[558, 20, 488, 7, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[1071, 31, 611, 8, 29, "Subsubsection"], Cell[CellGroupData[{ Cell[1707, 43, 4904, 115, 464, "Input"], Cell[6614, 160, 601, 8, 28, "Output"], Cell[7218, 170, 754, 12, 28, "Output"], Cell[7975, 184, 597, 8, 28, "Output"], Cell[8575, 194, 604, 8, 28, "Output"], Cell[9182, 204, 602, 8, 28, "Output"], Cell[9787, 214, 614, 8, 28, "Output"], Cell[10404, 224, 617, 8, 28, "Output"], Cell[11024, 234, 618, 8, 32, "Output"], Cell[11645, 244, 618, 8, 32, "Output"], Cell[12266, 254, 615, 8, 28, "Output"], Cell[12884, 264, 615, 8, 28, "Output"], Cell[13502, 274, 617, 8, 32, "Output"], Cell[14122, 284, 619, 8, 32, "Output"], Cell[14744, 294, 617, 8, 28, "Output"], Cell[15364, 304, 615, 8, 28, "Output"] }, Open ]] }, Open ]], Cell[16006, 316, 681, 9, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[16712, 329, 457, 6, 36, "Subsection"], Cell[CellGroupData[{ Cell[17194, 339, 16005, 244, 249, "Input"], Cell[33202, 585, 593, 9, 28, "Output"], Cell[33798, 596, 592, 9, 28, "Output"], Cell[34393, 607, 581, 9, 28, "Output"], Cell[34977, 618, 581, 9, 28, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[35595, 632, 635, 9, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[36255, 645, 2080, 58, 279, "Input"], Cell[38338, 705, 528, 7, 28, "Output"], Cell[38869, 714, 523, 7, 28, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[39429, 726, 2813, 61, 248, "Input"], Cell[42245, 789, 1434, 20, 28, "Output"], Cell[43682, 811, 1440, 20, 28, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[45159, 836, 1671, 45, 223, "Input"], Cell[46833, 883, 456, 6, 28, "Output"], Cell[47292, 891, 458, 6, 28, "Output"], Cell[47753, 899, 443, 6, 28, "Output"], Cell[48199, 907, 457, 6, 28, "Output"], Cell[48659, 915, 445, 6, 28, "Output"] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)