(* 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[ 52604, 1205] NotebookOptionsPosition[ 51091, 1148] NotebookOutlinePosition[ 51500, 1166] CellTagsIndexPosition[ 51457, 1163] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["MAP30#1 \[LongDash] Reliability of a four-engined aircraft", \ "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}, { 3.918652331601612*^9, 3.9186523327264338`*^9}}], Cell[CellGroupData[{ Cell["\<\ Question 1 (Reliability block) diagram\ \>", "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}, {3.918652303113649*^9, 3.9186523501265917`*^9}, { 3.9186525611043043`*^9, 3.918652561653429*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Show", "[", RowBox[{"Graphics", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"2", ",", RowBox[{"-", "2"}]}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"7", ",", "2"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"7", ",", RowBox[{"-", "2"}]}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<1\>\"", ",", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<2\>\"", ",", RowBox[{"{", RowBox[{"2", ",", RowBox[{"-", "2"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<3\>\"", ",", RowBox[{"{", RowBox[{"7", ",", "2"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<4\>\"", ",", RowBox[{"{", RowBox[{"7", ",", RowBox[{"-", "2"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"4", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"5", ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"9", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"10", ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"4", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"5", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"5", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"9", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"9", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"9", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"9", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "2"}]}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"3", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", RowBox[{"-", "2"}]}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"6", ",", RowBox[{"-", "2"}]}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"8", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"9", ",", RowBox[{"-", "2"}]}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"6", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"8", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"9", ",", "2"}], "}"}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], "]"}]], "Input", CellChangeTimes->{{3.608196740367448*^9, 3.608196753251458*^9}, { 3.608196789359242*^9, 3.608196914843504*^9}, {3.8866635020392427`*^9, 3.8866638554757957`*^9}, {3.8866639215155153`*^9, 3.886664287744197*^9}, { 3.918562376806148*^9, 3.918562581566321*^9}, {3.918562621143326*^9, 3.91856276871804*^9}}], Cell[BoxData[ GraphicsBox[{CircleBox[{2, 2}], CircleBox[{2, -2}], CircleBox[{7, 2}], CircleBox[{7, -2}], InsetBox["\<\"1\"\>", {2, 2}], InsetBox["\<\"2\"\>", {2, -2}], InsetBox["\<\"3\"\>", {7, 2}], InsetBox["\<\"4\"\>", {7, -2}], LineBox[{{-1, 0}, {0, 0}}], LineBox[{{4, 0}, {5, 0}}], LineBox[{{9, 0}, {10, 0}}], LineBox[{{0, -2}, {0, 2}}], LineBox[{{4, -2}, {4, 2}}], LineBox[{{5, -2}, {5, 2}}], LineBox[{{5, -2}, {5, 2}}], LineBox[{{9, -2}, {9, 2}}], LineBox[{{9, -2}, {9, 2}}], LineBox[{{0, 2}, {1, 2}}], LineBox[{{3, 2}, {4, 2}}], LineBox[{{0, -2}, {1, -2}}], LineBox[{{3, -2}, {4, -2}}], LineBox[{{5, -2}, {6, -2}}], LineBox[{{8, -2}, {9, -2}}], LineBox[{{5, 2}, {6, 2}}], LineBox[{{8, 2}, {9, 2}}]}]], "Output", CellChangeTimes->{ 3.886663490143381*^9, {3.886663674020823*^9, 3.886663734603846*^9}, 3.886663792160627*^9, {3.886663844215858*^9, 3.886663857297524*^9}, 3.886663945725881*^9, {3.886663976015362*^9, 3.8866640130167294`*^9}, { 3.8866640475703583`*^9, 3.886664057520357*^9}, {3.886664114756781*^9, 3.886664130285997*^9}, {3.886664171136074*^9, 3.886664192295781*^9}, { 3.8866642338391523`*^9, 3.886664279282569*^9}, {3.9185624088495407`*^9, 3.91856251173628*^9}, {3.918562554899534*^9, 3.918562582437889*^9}, { 3.9185626520757427`*^9, 3.918562705672036*^9}, {3.918562740900341*^9, 3.91856276954985*^9}, 3.9186523808144197`*^9, 3.918652626751519*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Reliability", "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}, {3.918652303113649*^9, 3.91865236732623*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearAll", "[", "\"\\"", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[ScriptCapitalR]aircraft", "=", RowBox[{"ReliabilityDistribution", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"X1", "\[Or]", "X2"}], ")"}], "\[And]", RowBox[{"(", RowBox[{"X3", "\[Or]", "X4"}], ")"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"X1", ",", RowBox[{"BernoulliDistribution", "[", "p1", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"X2", ",", RowBox[{"BernoulliDistribution", "[", "p2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"X3", ",", RowBox[{"BernoulliDistribution", "[", "p3", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"X4", ",", RowBox[{"BernoulliDistribution", "[", "p4", "]"}]}], "}"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Mean", "[", "\[ScriptCapitalR]aircraft", "]"}]}], "Input", CellChangeTimes->{ 3.728987454155408*^9, {3.8866630499093018`*^9, 3.8866631065763187`*^9}, { 3.8866631474618673`*^9, 3.8866632949709387`*^9}, {3.886666467050343*^9, 3.886666472168633*^9}, {3.8868196813306293`*^9, 3.886819687605598*^9}, { 3.9185644870269613`*^9, 3.9185645144258947`*^9}, {3.918564586716218*^9, 3.9185646373399973`*^9}, {3.918564692940502*^9, 3.918564740791957*^9}, { 3.918564773417501*^9, 3.918564807504076*^9}, {3.9185653003953857`*^9, 3.918565343473784*^9}, {3.918652384140719*^9, 3.918652384976371*^9}}, CellID->522227289], Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "p1"}], "-", "p2", "+", RowBox[{"p1", " ", "p2"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "p3"}], "-", "p4", "+", RowBox[{"p3", " ", "p4"}]}], ")"}]}]], "Output", CellChangeTimes->{ 3.8866632462219687`*^9, 3.886663327579009*^9, 3.8866664730382547`*^9, 3.886666505051875*^9, 3.886819735317889*^9, 3.88720329573217*^9, { 3.918564624161817*^9, 3.9185646382243357`*^9}, {3.9185647024160843`*^9, 3.918564741640629*^9}, {3.9185647766922207`*^9, 3.918564808180202*^9}, 3.918565308805544*^9, 3.918565344817225*^9, 3.918652385926735*^9, 3.918652630631145*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Reliability importance of engine 1", "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}, {3.918652303113649*^9, 3.918652404726491*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ SubscriptBox["\[PartialD]", "p1"], " ", RowBox[{"Mean", "[", "\[ScriptCapitalR]aircraft", "]"}]}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "p2"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "p3"}], "-", "p4", "+", RowBox[{"p3", " ", "p4"}]}], ")"}]}]], "Output", CellChangeTimes->{3.918652632572958*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Upper bounds, etc.", "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}, {3.918652303113649*^9, 3.918652419426537*^9}, { 3.918652504540345*^9, 3.918652505277317*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"p1", "=", RowBox[{"p2", "=", RowBox[{"p3", "=", RowBox[{"p4", "=", "p"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"U68", "[", "p_", "]"}], "=", RowBox[{"1", "-", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["p", "2"]}], ")"}], "4"]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"U70", "[", "p_", "]"}], "=", RowBox[{"1", "-", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "p"}], ")"}], "2"]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"r", "[", "p_", "]"}], "=", RowBox[{"Mean", "[", "\[ScriptCapitalR]aircraft", "]"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"r", "[", "0.9", "]"}], "\[IndentingNewLine]", RowBox[{"U68", "[", "0.9", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"U70", "[", "0.9", "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"U68", "[", "p", "]"}], ",", RowBox[{"r", "[", "p", "]"}], ",", RowBox[{"U70", "[", "p", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"p", ",", "0", ",", "1"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"PlotLegends", "\[Rule]", RowBox[{"Placed", "[", RowBox[{ RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}], ",", "Right"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Red", ",", "Green", ",", "Blue"}], "}"}]}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.886653879874362*^9, 3.886653907183597*^9}, { 3.886654081551045*^9, 3.8866542085694723`*^9}, {3.886654239625498*^9, 3.8866542856528473`*^9}, {3.886654365056555*^9, 3.886654368041767*^9}, { 3.886654545729435*^9, 3.886654650307076*^9}, {3.886654690821553*^9, 3.886654731198338*^9}, {3.886819694772443*^9, 3.886819731475019*^9}, { 3.8872032711328583`*^9, 3.887203292181191*^9}, {3.9185654675965967`*^9, 3.918565500733658*^9}, {3.91856556473543*^9, 3.918565608047085*^9}, 3.918565661924109*^9, {3.918565745111733*^9, 3.918565757935938*^9}, { 3.918565830050785*^9, 3.918565894537519*^9}, {3.918565962600662*^9, 3.9185659741250753`*^9}, {3.9186525167285624`*^9, 3.918652522902781*^9}}], Cell[BoxData[ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "p"}], "+", SuperscriptBox["p", "2"]}], ")"}], "2"]], "Output", CellChangeTimes->{ 3.886654209613905*^9, {3.886654286611533*^9, 3.886654304186021*^9}, 3.886654474752037*^9, {3.886654610235767*^9, 3.8866546652038116`*^9}, { 3.88665472586182*^9, 3.886654731992627*^9}, {3.886819732601428*^9, 3.886819736842751*^9}, 3.887203298083955*^9, 3.918565664580105*^9, 3.918565758797106*^9, {3.918565878042244*^9, 3.9185658950717907`*^9}, 3.918565974749928*^9, 3.918652523795926*^9, {3.918652634194561*^9, 3.918652639520688*^9}}], Cell[BoxData["0.9801`"], "Output", CellChangeTimes->{ 3.886654209613905*^9, {3.886654286611533*^9, 3.886654304186021*^9}, 3.886654474752037*^9, {3.886654610235767*^9, 3.8866546652038116`*^9}, { 3.88665472586182*^9, 3.886654731992627*^9}, {3.886819732601428*^9, 3.886819736842751*^9}, 3.887203298083955*^9, 3.918565664580105*^9, 3.918565758797106*^9, {3.918565878042244*^9, 3.9185658950717907`*^9}, 3.918565974749928*^9, 3.918652523795926*^9, {3.918652634194561*^9, 3.918652639523284*^9}}], Cell[BoxData["0.99869679`"], "Output", CellChangeTimes->{ 3.886654209613905*^9, {3.886654286611533*^9, 3.886654304186021*^9}, 3.886654474752037*^9, {3.886654610235767*^9, 3.8866546652038116`*^9}, { 3.88665472586182*^9, 3.886654731992627*^9}, {3.886819732601428*^9, 3.886819736842751*^9}, 3.887203298083955*^9, 3.918565664580105*^9, 3.918565758797106*^9, {3.918565878042244*^9, 3.9185658950717907`*^9}, 3.918565974749928*^9, 3.918652523795926*^9, {3.918652634194561*^9, 3.91865263952524*^9}}], Cell[BoxData["0.99`"], "Output", CellChangeTimes->{ 3.886654209613905*^9, {3.886654286611533*^9, 3.886654304186021*^9}, 3.886654474752037*^9, {3.886654610235767*^9, 3.8866546652038116`*^9}, { 3.88665472586182*^9, 3.886654731992627*^9}, {3.886819732601428*^9, 3.886819736842751*^9}, 3.887203298083955*^9, 3.918565664580105*^9, 3.918565758797106*^9, {3.918565878042244*^9, 3.9185658950717907`*^9}, 3.918565974749928*^9, 3.918652523795926*^9, {3.918652634194561*^9, 3.918652639527193*^9}}], Cell[BoxData[ TemplateBox[{GraphicsBox[{{{}, {}, { Directive[ Opacity[1.], AbsoluteThickness[1.6], RGBColor[1, 0, 0]], LineBox[CompressedData[" 1:eJwl2Hc8le//B/ATDZ+QkgolI0QyMirivFWohBQZpZK9E5I9U9mHREY2GYUk hOxQlD2SMrLOum9ZZZTvdX6/88/9eD6u676v+1r39XocQbM7VyyZCASCxSYC gXHVtJztridfJRL+7zemPFNkYDbKIw8EgsDOIdVE4l7W/qg3PGrILGCr+o74 rtbP4b6oDnJc+0WbDqKUIlfOcx59ZCZzadWvRMJu8pMNfmPkzy28VT+J3bT3 QbdFbyJz2O63oREvm3+svB1/G/mbLtvVBaJSl1xJLI8FEAJKc1lUV4iHVFJf NKVYoXKMnWlpg8hWwJK2yG+LyrdNrr1jhsW9rvEiWfbIuwLcfmyD78HfIw1E nVB9O0uKNRuY/8lqbNJ3BkL9s1Cpwp0wKGVMNIm/C4T0vH9T+ruhPrlJIZLH DQhj/BxfgAfkezxei1y/BwRTJ6Z/AQcgn0VKsjbFHQiq75oKFvkh9t4zYZzf EwikkzE17w7B1pfa6Y9ue6HneS1p1YmA1wTTAYEsbyDIdFN5fxwG80uOuy+L +qH2mZOdrI/CUIhQNNnaHwglzL0L3VIg+sN+S4N+ABC6ij8PF8hAEpdgoHF8 IBDyrvxw15eD4MBwjzCeB0AQ8xrbDYpQe8Cq3KAKucvnkdpXJfhToboodD0E lTce4wxQBgds6U51ykPG+PQGLwDoXze1pvGHAmHd1Pp75VmIWlbKqaxHpi1x WFeqQVvMnp8PbocBQQuzI9aqg0rbp5t8WeFAiBBo6h85B6IKCgY6olGoPlNW lqUWmHZxxPG2Ij/bFZaQoA3J9pTuaeto9Pzgw0OdOsDS3Zlbp08CwhlR37R8 XfDZFiJkFB8DBIOCB51X9MDCDecJ5YkDwstJm7PKxiDHHOtV6oyc2+z6lfsa MMXKf/vWilwvVSO4cg3Sij1TpNyfAsHjCKmt2QSGKcz8fT3xQAhtWlFQM4VL t7mF+SMSgfD2U7O7qQUcnKt6cP4n8tiKvhbNAmh+N6buKiWh9cD1d8XTEsJS MnObZ5H9ZjS/J1lB8+BRcTv1FCA4FrY1zNuAks5pqbf/UoHAtjA6t+oILN9/ Rv24mgaEqIQ6YrYTDNo/xLe9Qn7S4mJ+6Q5UNVsavZJMhwDXQ77PrjqD0UQB D2EEWffvVseauxDLp5CSczITrafj9YfL3YAl7kLG3K9sICy7m4cZe8PayfG1 DN4cCHi1N+9Xkzdg3z0M9M7mAOFmToOwtA/0Hs5jLY9D5Wa1Z7BtvpBavdXd +0QuBMjtE2Jv8gP5n02aW31fAGFfYWKFdCCYyhIX97MUQADXLTs57hDQG+zX +SxTAIRIctG+ayGg4eOY72eM/Lxg8+2UEJBoSbk5XoDqC+R+EBJ6CMvGa225 2oUQ0DrUelv2EUQEVj4/9uQlqD68stpiGQoVXbLnzh0shvo7duJL+6Igikw7 f1QD2V770LhFFFgxvdDc5VQMBN9ENcnSKNgrv1/n23vk01nfprSjobo9sKBC qgRMRY3KqWok2C9t9/rilxJI/0Y4PRwaA8NLSnWu7KWg2uHfFn4iDjSYuFWt BEtBQDmnYM08Dkp3LNUbKZRCPZ8dRzIpDsIOFzeq3EDlbPraNpQ4UDI+1LLt FSo34dqlnP4UEmtYPydrvYF0q/fXmrkSwCh4ZLgpvAwIF0rW5QSTYOeY6FHr jDJIZ6uo6zJMgo/Kd323V6DyMnJudlQSKC1vEbg8gbwj78Ov9STYbytt+ePk W6gv7PMVGEmGHzpB+J+pt2DqdibiY/ZzsOAV2yylWgGm6k6i4cXpcOe1q+Sz xXdQfzDMY74qGzDl8d6PLFUwdjz8Rv1wNji06XitHaiC9FO37HJWs8FmVLz1 pnoVOFeo0suUcsCUfcxUJB7VH0iVI1fngK6tVlzpiWqQcdv1LKsxF2QERdY6 vGrAeTptUn08D+ZJA22bNtVB/YaCk63ZK2hraKnrVG6EIRWLjG/iZWDreYHd mNYMz3wmWqvPV0HDf7IbLx1bwURF0N34Uj3kZjX/4xX5BKTzCnF5HM2guvd9 pl5RB2TzdVhG9beCZOtIZcuRTtBP33gz09gOfap6WD7WBY8/+UQV83eBw3b7 nn6ZHugaJzlV6/RA+5Dh+x1RvUA4fiw6qaEP9DSMxicn+8AmnRL9WHEQjqeH G6YLDwCnpv+oa8xXGPv3pM/GfxCExJ+07Ds0AlMXOrP2Ng3BY9K1ntPhP6Ak cdSzW3AYeL6I91vFjkHOY+ZQca9vMMDOFFzXPw5L5tcoVtUjQM8umbT5NwGs ag+vvN73A2pcJQojT06Cz84ptnGTUeCavDu/9eoUsNVKEAa1x8Al3y+dy2wa VNwv/W1aHYObqTv6b3jOQEp2RNahlHH4Xi5aOeA8Czevyn/+7+IEtFQ5qtg4 kuFtv+WT2uUJOMIZtPWOPgUUO0qYpuN/gmEuKW7zASoIqFstPVGbhKgPEoH+ E1RQkFeIKZuehG7K/RukMBqMzkd+zAqZgnKh8uqd/HSgyV0O4ZGdhuEdN/u4 i+ggSpWkbOqdhnzOd0XfhDBoFr7X4xw4Ay67vZS7ozEIflFltB48AwtNPN4a MRicOUIYffRwBgadJj5UxWLQIB1OTQ2fASdyXUD6UwxqlTI2f346A34yTjGm yRhU6H4+Ll4wA4nR57Tf5GJQ4COSPN4zAxW7515l12AQ3ddvfkV4FoI8ODOa pjCI8IsU7hadhSnR476/pzEIE1OfuiQ+C5zSEz5HZjEI8Smz0paaBeHZxplI Cgbewk9sz5+chX+Tyi6aOAbWbrp3iFro/rtno5P+YABc7V5H3GZhhxdv8rPt OOB69TFMzbMQsdLFxHsUh+UXIQ4VLbMwvr1fUUoSh39rmuccPs5Coa5HwGkp HNiy+9f7v8yCFOc/FUsZHMQWKdb5X2fhslBNcIY8DqZxe4i6+CyQR7Ue05Vx 6OqzozznJYMsqfxXvxYOg2IyH67wkUEj27K9QxuHHz5LadsEyDCqyVvfqIMD TTjg6l0RMtxlZV8v1MWB5d7TejUZMnzff6fNVR+H03vq46nqZJC0sNv69ToO pVf3nFW8SwaWRuGqdVscYjn8Z+tcybBDrpD3ox0OLh9nIzXcyUCrhNo4exyO qdQM6XmTwUV1oFPcEYcSYXMnpxAyZLnFi1x0xqFooSQxK5EMFSxFE3buOBTE aM2xN5Kh8ILnT4EgHMIulj+Na0btHfJWG0C22yJwan8rGaY2j8yHBeMg7rkQ ItZBBozIpjj/AIc806T9ZwfIQOq3dKt8hEOu9KyGB4UMzoNavw5F4pD1Ofj5 BCcFekMjr3sm4BBxbM0kbQ8F6tYfmYk+w8H9qcsBE24KdP68ld2DfP7G7eR+ Pgr8YLEcFkvCAaMRE9vEKHBDfXl/RwoOJ9lW44qIFNijLWyIZeDwWdM5wsuO At4hB5uyC3EoL5q5eMKRApMK/huKL3FI57zFuniHAt8CRx58QXYZ1g5zvEeB 8yOGDkuvcOC2k3hsGkCBwaCfVUolOJiFTgdrxFOA/6tEdVYZDr9bTbw5GylQ obHVbb4Gh4N6GvcamylgkjZw6857HDR+SN9xaUXvu6GYT0WOX2Qy7+mggNkJ d4OJWhzkBfM1YwcpwFmAibbVo/a9lng46RQYPW2xyb0ZrYejUZW7uKmwlexR eKMdB67K+6UNvFRQW2MSakU+dfb2y7t8VFD3PbhZpgPNj7F8ercQFS586mAj fEbz8XD4UYwkFfScbygnfsHBalTUcNdZKswTDt0v6cZhLKZuaacTFV5utnC9 N4gcpF0V60wFstxFg1bkcddvflyuVBicv9zMPYTDxNXf27g9qBD+WupsFfJP Hmle/iAqZEcoDvz+isN0RipRMp4Kb8+fyrwxggP1te+jC7VU+FB22HBgDPUn k1WrvZ4K6yGxurzjyE8Sd2o3UYFUlDF2g+F7bxN126ggKsHX8hMZU6QXGvZQ QWrjWQllAoe5BpMuy2kqyFH36k9Nov3afYonaAcNCP6phqRZHOWqwd+Ku2gg 3rwS0IG8ncV14NduGmQ+WjnFQkbzQyx4cpuHBrW5FTZ+yOoF3DtOC9NAjvdn viUFh7igJSaCEg265xxlBGg4pPLFjFco02Bu3a3gKnJe5dH6O0ADe4Ob78OQ azBz31E1GsRL5hQvIE9e6/lde4kG7/ek9NTTcZCTK6b5WtLgn/xb9/M4Dspf NNsVbGiAYS1l95E1bKfz6XY0YBOaic1FvpbGZ33DmQbRgvuPMc/hEMQaMa7s TYOD7z9sqkTu+WkzsEaiQYOth+HOeRyc44TqPWtosOCXTPZbxOHKUzNb5joa qDCbZqQjK8RnckY20GBRrH5XI/JqgpBlegsNQm5W821ewiEkWWh7axcNQg86 0x4gJ2UK6XNN0eBiyu43nss4+GSZ/X0+Q4OMzsiDCci3sjNzD1NQf3+fOF+G LJwrtKKE06Au0HeQjlycL5R6e4UGrJXO+I3fODSXCM0WsdOh1rrksuwftP9f m8Wc3EmHtZGrHy8ih5ZmKjVy0mEKsjZbIuuUCUX276PDq+jo1njkrxVCsuuC dMjz2P/4NzJWK+Rz4TgdLjasEYtWcNj3WWjn5E06DKVE9M2vov2/1LdgepsO 3exH/tuyhoMR36PB7+Z02J5HZt+HnORITR20oYP45s2hSsgHd5RJtrvQgW+Q XccfWfSS+sXSh3SAvcoGhHUczt3/LSUdSodLul9LOJBt0vI5X4bTwXjZeOwg cgHOPpxDosOCjUydMrIUacAmMYkOcRxXH7gjK3RbPwxA56qiC5vjBLLBCo/d 3xI6qEuRTuLI7oId2l5v6OBZFf19Dbnyrswet0o6EGyE3nL9ReuFcyXLupEO wXKOmWrIanphDToDdLBzrXrzHNnSWzmnfQi9f5rpyTzkh1nY4/Pf6MBxBksq RW5buKJ7ZowOB4z7VluQteL2jypQUH/+XJLEkPX6X64f+Ieedzro2fF/OPi9 cFjtJGDg12rYC8h5nkf/BDFjcF+ejXoeeZ3v5cIsCwZ9Jmal15BzrQopZbsx aMJm8n2Qu07az1rvxWCtZLjvAfLadolpXh4M/DfURyOQdYsLxgMOYtDr9flJ CvLq7/whLXEMnqUHPqhCFv5kO7AhgYFO1IGyBuRLKeJ9pVIYOCeXf2hDzlbN 7+SWx0DzsQhpAFknNK9lkohBjlb4pznkTN4XZT76GEyvXuIR2MChg2ZVKm2I wSZDm0gR5N+1oiUTxhg6p3VnjyBrmecWnr+FAb/tOz0F5OXCnEwuOwwWfZZZ LiAL+FmmtzpgQFBOqtZGvqgrkup1BwM1RwPDK8jpi9mJY24YjI8pXLyOrKmS TXrpj3KQi/ZRB2Q3DouoW0FoPBNcpZ2R08YPRXCGYJB4d5LPDXkxJOuRRxgG B5Iq33sjp37J9FNDuSktOX5nGPL8rQyHkQIMrrpcVslCXkrYonD7FQZxSraT Och/Om3/ThWjHGTM6puHvAGyUXgZBl/2VQW/QmYTaCpmqsNgm+lpWjkyh9Fh j0cNGCyXSYq8Q+YkhauyNWPQnih3uRqZm6DfvecjBqnL2sF1yCJjk/NivRh8 37Gi34osxn2h+lU/Bkq75yQ+Ih/VfRUsO4T66+Tz+xOybP09LuXvGJSIsjt+ QSambz1+aQaDzNbNg33Ip4fs/vWSMYidSDUcQFbb2dliRMOgcfvxL4OM8Q1I MDT7hcGK+n+pw8hGpmKe99ZQ+76/OkaRrz+LOL36FwPJa8JM48g3u+b+8yfg cO/cC6kJZEvVd0mPt+AQFaXqNIls48Fnzs6CvtNFLwKnkB1KAiViUe5bsidE TiO7CGjWJHOgHPREOGIW+Z5R0QMBThwSOYgBZGQPEqd2DhcOFZpTDhRkf8K3 70U86Bw3uSdDQ44Ys99oOIT2ieAbCxw5mrurVUMUB1ZpfcE55FhdeVK7GFqn xQWDDCfWrwv0o1zZdmKL7Dxyyh9TsjHKkfKLOgMMp8t8eP1DFocz4V/dFpBz 0yPPzJ7AoanhZMYicv7Qr+2OSjiUHdeVXkJ+udOg9xfKmUkyUpUMlwYctFg7 jcPHW3VVy8h1psUhO1DunB159fAPclWnw8UfKGeuZqqsMlxOPLKr6DL67mk+ tFlhPO9AToq2IQ6kiimFVeS8cDMzvmtoXD5oPWU4a5VfjG6CQ8IZ9jmGk4aS 3kSYoWuq/LM15PhzRp4mljjYs85MMRxTvgeO2qB1wxQmvY78OI70qR3lziNc shUMBzPrkJJR7uyd811i2M+F1cDeFQfmr+dk/jLmQ/fh+HZP1G7aSDLDznVn Xwx74/D3FrmDYQepTY4FfjgEYr9XGbZ+XivrFYhD5OvDov+Qzdh8/lxAOZTk nKDD8E1vxVoelEO99SzdGDamLAeTQ3HgmyhKYFi37S5HaDTah38PDzKsdUK6 3ygWfZfcohcYPpdLSxJ7itaFzQT7BvKZPQWmf1Bu7Tl5SpRh4gNr0TaUSwvT 3igzrLggTEt4jvr/xuIyw/JmE6+t09H9k1YWDMt0p90/kYWDykb3PYYlVG+o bMtF55zY+xCGRYt5mQfzcFAaI8YxLHRwqC0X5dg76w4ZDPNFPo1yL0Ln5EuT Vwxzr1/R13iN3tdDqJJhLvudvHtRTm091dPAMMfw59GpcrSPJPw/Mbz9QnjO 23c4bO061cPw1srz9iEox37dxvuVYabDW49drUP7eovEKMN/nzYtCzfiIKjj P8nwn82BNYsopzZUi5IZXnQlBjW3ovnylKEzjE+snYv7hPqxpXCOYcrld+wW KJeOHs1eYHi63r1Xrgt95zjElxkel5ZPZO5F48On8Yfhmhf8rYEop9WVBm8w nMDPusS4/v//xXPwPw+OoZ0= "]]}, { Directive[ Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 1, 0]], LineBox[CompressedData[" 1:eJwV1Hc81d8fB3BR0RYSGiRJw0glqe6LUKkoo8zMaKCSUUaiUMomSZIRlZSR XdlZZbvRsKno3ntUyJfkd3738biPz+P5+ePzOOd9Xq+zxvq8ni03FxdXH/3/ /3nQ9ntz6dAxRkZx5rqf3F27v704bt0tug38rvX5Xxj3GMILmCEvRTWQsdZg q/PuQkZhsbfDJWkdiKb0hT+wes+Q2ymU8kDUAMfrgiM1lT8yuASHImfEjTE4 8uyGVXY/o5n15pqVtDk+Kv6JrjRhMXRtagusoq0QajHh6XbwN0OlaWtmhOhJ FD/b/HGPwn+MtXviH1fE2SFte+7wza4ZxsI0voej4mcw5j+2KiqNB6PCztHr ku0xXPtTdryWF53XO4OPS5/DB40Cjp72QthMJJdXGFyAOFfNMa1YfrTLGTPM op1wS6SxowGCKL1fsT1Y1AVTjY/sTSVEsa3lctY6U1d48GvUHzRdiad8crLF cW7IahC/NFItjgjXGCki7o6ZycIny++vxdx07YQbVh6QaI917Li/Dh593Csl kj2hodafYZa7HjZHHAV1pb2xae7yBTGKm9HhLxk6dOoqTCxsDNSj5SDdZT+n zMAHGYmsPdqBCogVWuNrHO0LsaORtrEbt+K67+3Lt0T9oHXCaH0R104Ur7TL O17kh0Uf8nJYUSqYyFcdlTT1R9SyNQ9ObN8NB87Y+VdxAXjD71fIiQUMTC1P scQDMRq/t3+PlzpCxlVSCkoD8cju6On1lzRQE76s38/qFpaqGhlJXdbEnpo6 81XJt9EucCBWL2g/pLdvP64jHQKpXY0RhtOHYNm0JEqsOgTlljxmL2W0cd9+ uPnrqVCIu6xmCpvogK+5MbXEIAzMls9XLp06Ci9ef0mj6HA4vesNO8Glj5Mu RDRQNApnjbry3pQZYStPhEf2hShUdU3dEIgxBnfEts+fq6Pg8Icra8DJBA8z 3OPk3O6gjNvCYFreDJ+GecTbWqLRYK7yfZBpgSNWIlLiQfdwoV7fpq/fBqtH ivwO9N9Dh3D2SMnZk2B5nxh0UonF2/gfZQa/T+JWXFJq5fdYZF3VN0yaZ4fK 9s0bzmrG4fASjk3pwdNQ0VGTy/0Xj6ej35gJqx3B19kf0nXsIWRCRvVflTqi 3T6A8D5/iH/Dywr8T55DUaWt0XPZBMzcCDGTyToPo740Ua4vCSA75cUPyzsh YtX2uBTlJPx9Xd3fOdsFfFFaiSM/H2Frk3ko0fHAlHLvVKJYCj7MtDOtXnqA 03n5uL56CvbFfuC9JeKJ1vVPFuRFpeDihQ1OUwOeiH81181zRypYI3ayJwKu YFt/xcG5Vx7Tdd+54u7qA0tFxugKvjQUNwSILFnlB/12pk69Qhq4VoxquJv4 YZ+X41Nv4zQo5Y277orxw6aqOPPetDSwIkVvVgv5Y9x4qiZV+xnqPrZ2Ti0N QJBvwYMtkeloPeveWbryJvKbFPfvX50BzWg3XlHnIIQMsQ5s3peB0jazyeHC INhxPz649FwG3i+MLFo8KxjC21bofH6TAfWQhEOHwoLx6p1vWr5cJpq0r2hH Z4dghfzZrEMNmQh8uchS4XoYPo2plDgvyoaPkOfD5WMRMLr+5VPF7RxkfCkq n9KJAX+P9OZTiTkQEmC8XuMTg9rdTlfm5+dgWvvnY5esGKiMz5HQ7csB6TYU TxS6hxVn5G27lHOh9tGTX7DzHrp0rpGJwVzIyY0IHHG7j5NiMrPlVPORKs0O q6mNx/ksZ9mY0UK4a04++TqRhF9hH2pmzSqBUqa0Y+u1NNSUVZU07i4H987O A96cLJxx11pkzKqE5VCTjp5APsrmKc6kO1bD/KzMDZOjr5GaXPlPbF0d5Kz1 xW8ol0FV+E2S/ov3EEs9HdWqUQnZ6i8FVRsboVvhLyN0thptqvqcp5wmNBuv lC2dqoPDfPsWpkIL5mV8TBZ2asC7DsM3i0NacUZE0zBzfTP09xn1Dgy0wWd1 7OgbsVYoJdw2TJD6gNNa3BLBY23o+RfZdvpqOwInF8de4mrHoFZjsnBFB57G rThE2B3IvNft3rzmE26W6xbv4/uMlJs8gRs8PuOT9Q5xHbFOjNmYDNu9+gJp wcLyHXzdWKARoJe1vAvP9uWpR4T0wIt/cGGvWTdkteW5Nf17sbB4E1e7dg9U P2vD0qUPe9yOTFdM9kCldP6fDud+xD0KSl4b14skgQulDScGYH5sW/28Q304 tbV7IvfYIHKZtpHF433Q6Ll9IWzvV+x8n8n9NbofL70k+P+KfIOEpt1YpMYA arNPjBf99w3bt20Pz/k6AJUUZmpcxXd0/wquTfYfhIdPcmGo7xBYW3X9RRW/ wpS5q0px3zCkf8gOz2r9CrMCjXmao8OolHJtueD7DTsclLAt9QdC25g2elLf 4aHswF+nxgLRLw3nrvyOizIaprxNLGQfW6a+02kINi4J123M2Uiuv/6gT2AY 0b+mA/La2fhTbeYpUD6MWOuJATUdDnrCS8b4z/2A6AvvD3tyORhv3iV6bTEL m/L/eS2fR8Dl2P5n51IWmgSWdJyeTzCfz/nDT0EWPlWf1C1cQLCakRZpJcqC nnhKvOFiAs00kcVqUizcGupMDBQkiLo2xs2lwkJEhgujYhXB1q0ZrCu2LNSE uTkEbSG4ECVZ6v6aBYF684fOxwn07lif4SlhYe+SDD93Q4Lt0UkCwWUsCOrq JHkbEUzelbRNqGLhJp9eQIAJgf99yfnVdN9qjsYjQeYEsUmSBkKDLOS+/aTu YkdQmSn5/cUiNrLymCnprgSpWdbhyvxsqF3Vu3bPjSAwO0mlXIAN43LOHf9L BDo5ksHM5WwENFlZm7oTfMyXVPy7hg0Re+XQaS8CTrGkl5YSG9eXjCqs9CNY Xi/JP0Dn/GdRolF5OIHyWNtvSys2ioJae8IjCIxW3WjvtGFD6dvPVMtIuj7H H/Htp+n3ZrexpqLo/BbnyL67yEa/qpn5hhgC6SOah7ID2LjkzNtiEU/333wq wOcFm94jd2tV0giO/yd6djqTDQ+O/Kxf1G5r3mt7vGRjbmuT65NnBAVOCstc Ctj4mMAvLPicYLfAf8mnytl48qFxS3cGgYb+rTKdD2zYuyU06eUS6DPT/678 x8bfv4lXH5cQeD92mGzk4uDk282l+qUET9w3T1zj4cBLWltshvrvqvTf3/k4 kDqxZYV+OZ2n3bPhHEEOEi++1hmppOfz52nH4Q0cIOaR20wtQZLY4xwvAw56 xbljL7QSvGfZZcsbcjB2u2pmhvpPsXRmnzEHXV8OeIe0ERy2SX12wIIDt+Zz b58wCcafpSQJneXAL+uuZ0s7wcE9j8LSr3LgoLfr2uRngl8WiQ5f0jhwr6xs jusnGLs7Z7vVcw4ui8s94h0gmGg8Mz2YwcHa8sR0J+oZKIaQHA50VsRYqA8S LJSoyOAu4WClo4F251eCdT0Dv2RaOVjeUqzxY4hARkTr1XMmB0tP8bhpDRNs Pvr8umIHB0pJwp2p1IqlrkK7OznI33j/sMUPAkbCXKUj3zhQmPcms4pFz99S xt11igPBfp9b5wmBaUyQ2uQ0Bx5bxJeXUZs3jcy7ykVzw2/0cekIga1qYezN OQQmvsH/MqkvShx8fX8Jwd4fOe8GfxIE9djPlK2lOTntdW7DKEGoSFP1Pmma 2zR7/XPUEUe3hb2TIUj5VeOYTX2v9K8EU5bAxbNir/IYPa+E4L3fdxDMNnV2 VBknKLHM8F98mIDH50WFyARBUaPDoS4d2vMtRp6G1HmMjUtf6BKMpNsq3aFO X5kSp017WfwwIW/RfzTPHbEvg6wJwlW0un9RR+83cjezJUgsrMjaMEnf5y3D 5tN0zmeCblhQ34wKq3vnSPd39t/uGmrXowG982nPQrgkG4On6H1Qov74kyfN aVHdq9fUDnKzHNO86br+vHg2TG290GtCi/aOEbDmjvpfgqM1TksCQwn4d7uF DFEf3iHPNKK9U15YHsU/TbA/lRUrc4d+J3FnvBI1w++UdE0sAcRSiq5Sb1I9 sYc3lSChiSE69x+da4YYT/sTgh3cRcrrqCVXd9Sk0l4tkDEwVacW+atnsC+L 7q+q+6kXtZA9v5hwDkHD3QbmXeoln+q7B/PofBe3z86mnltwwN7/NV3HCgWH fmru9XO3HKM9u3Ta+9Ek9fSdinEp2qPJqt5u/hmCUWfGtcpqgo0p/RYq1KRv an9UHUGuss8jbeph3cJFJ+sJDOfIsSyoe+W33eOhPfL+VejnS/0l/qd5K+1N sl80M4y6Y1GGVHIHgfBW3w0PqVu9HIYv0t6M6bv7pFM3/NiQubeLrlvL+1MB dZ3JN1eBXnrPXQ3dUUn9tvbRrj7aqxan9LsN1KXK1rOyaU+yktsm26lfPxav 9qU9UU3lteqhLhDuDNKlue9Zpln3jfqlf6zeGprznNggJQ71i1FDkZ80xxHf O1N+U6fZLOsqpTnlK1EWmaBOaWlJDvtDezMUFzxFnaAWdsaS5iSAMX/uP+q4 TG15BXpuaok+vjPUd8UXjP3/OTHz/x/B/wAaTT6h "]]}, { Directive[ Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 0, 1]], LineBox[CompressedData[" 1:eJwV1Hk4lXkbB/CDV4tUSOpoQ2qkRKKmzZdi7GVrMG0ITZYpTXrTLktUismU VF45YbKnM9Jmj5MlW5ZEOPbjnOdnjWR5fz3X9Vy/5/PPcz3Pfd/fW9nlhI2b OIvFekTvH6eZW291Xt9+Pfr4Ia/PTa8n7VeXVrYOWFaRBxazDaEwr+7Wc3qy 1LVDVi21w8Zt8vGP2HZgWWbE+Cq4YnvV5oy/2K648s4yafei08h7UKgbxj4N fbtPWiLpQAT43zh7nR2I2LdRvmasSLieJuxQdiROvuhXnNvDwZxI08cDg0/g tEtf1jCQixdV2sbGK9MxoLhJdtOGHDgENDcV3uCCdy3WPTO7ECee/akRNfIS jQ2l/83j8DAUXs8TE8vFSKl4hItSBXj5xbmVOwuQZF2koDNQheN+pvMdhUV4 FdjNhG+pRf5c7ZkU7xKcqw0X8kzqkMApmlZcU4p6HR2Vm34N0Fd4G2ebVg4P DfvHr/77CRolzdnF6pUQdzU5dfTIZ3zUt2WeMlUQrm7pCHRpgZeUZ02dVg2U WocVF2xpRVmj/dsFt2ohMebJNYxog+0vDu2dnR8R8nhgbtH5dmyJvWEfq1qP K9f8cqb38dE2fefj75cbwFtZu19JswNdppUchcJGnPVxqSwa70DG/Va/auUm BCyT8JlX3on4EInQdec+Q+D83XN9ZBdGj/4mcH/djAGHskB7k27MMwy2ebbk C85IqlVH/KcHF2S6pNsPtoLfcS8+NrUH0jnrWQ2WbdBzrk9kW/Zi15l9U4UT bYhaYcpXGO7Fwyc3OasftmPWrWdhx6714fB+nYq55nxUd0Y9GlcS4N86tzs5 X/kw6TyhfjZDgG3lGeLddztQvMZ5X61mP5SM3EfvGHZiFyeM1ZzZD10d3Qhu dye0EozWhKwVonUo7D0nqAuvGysvZkYIIdxsHcTW7sZW3sUAsRkh1vZrCMRq u6HgsLza57AIRaq+NSf9exBtubm1MEeE2x/rjtqo9sJMLWtsRpYBsc2LEC/q xWp/96dWhxhk7l+8Z5tPH0yWhJ4cT2TAqQh4xJcToM/1c93cHgZjJQfPyxUI 4OSoxGioErRF5I7K/NEPrwPrsgUOBF+rd7CvLhBCevjY0P0AApZ3w9g2WSFE AaNbjQIJpOb8WT+4SIhEb7PZA9Qr9ZLuOLOFiDc322MYTGCUtHSBgaoQvE1x Wj0hBJFXR8VZ24VITshsU7hFsHlzuvCimxAC7V/vrogiOBmpkuf3RgijukR7 XhKBzd8uxyVyhXBCzFOLZALdu3FyYflCKAyERlZRT9xTcYstFsJijYFuQwpB 0AMVqZIq+r4vG+Na0wii41Ts5LuE6Lk1W70lk6AoQ6U3bb4Ive2pg9dfESQ8 c4n4WUYErVWWLuKvCUIz47YXyIkgy2n39KPey1UJq1siwv8uCUzd3xB8eqGi PaksgjDw/KYdOQRMjsoF0y0imHyITqvOJ1hSoSLTSfs02+6D0zMewc+jH4ed nEVIGSlrZL8ncFhxraHlqAh1Nfkif+po7/6Yht9F4BrfZaxKaf0WcDXKTonA WcQ3F5QRrN1nZJ4ZLIKFjqSvVCX9/+pjwVfS6BxE+fmz6gh+/cb2mMoQgfRd ijpIfUa53PLccxFizl6wyKbO9tFafDpbhNC9Tjf+qCfYKfeNc6xAhDvNpa71 DQSGttfz99aL8If/+uA7TQS2dSmTy6dFMGcUAwpbCS4lek1Ushh4tEhOsNsI /vHbMH5VgsHA9OHJE9STK1KGe+cw2PTpAEexndbTPVnAXcTguuDyOQ8+7c/Y 00aLdQwirvhYjnQSxCkmci/YMZj2mwjK6CMoF7pnatozEMtK9hinHstZm8F3 ZOClWtYEAYHF0YRkkyMMzkTZHaqg/pocHyfvwcClJaKf309gtutJeMplBreb /t0wLiIYOvLYqzmJgXEcx6BskGD0nqSucyqDV8u9ClhDBOOVx6e60hl8DuW2 6FLPQPsW4TJYt/NdRwy1tFJhungug1FWt4bXMMGats4htVoGpvPWvBoeIVBb avo6tY5BfIaQrzJKsMEqNUC7kUGGiU6CNbV2nq/8zhYG1VZ7JlOp9WJnbdlH c7Y736nb+Svtv5Oan+93BnyV+5lZYwQHom4aTEwx+Gn4SEAr9eGqgbmXWQTL shKY2eMEbvovo0MkCRbKcyPtqU8pmb15sJDgJ60PK4eob7Z5zuSvJpDrm1GX nyC4vbSq5Je1BAad7zhbqP+y0gkvU6NzVTPvhQP1/bxJpToNgq6gJakPqBNi w3b3bqV9sdzYsPw7Qa5TetACC4LGQ46rpScJXlV6mX/ZS7CvY/rqeuosPXXZ NGsCxw41VzPqlOXxDy3taZ1spZKDqaMbo5/fdCGIHRQ3/0Z919jB76AbQZp5 eZb8FEFE1mJs+J3mSknxiSZ1SGR4aZk3gcm2PRKu1L5Wwe1SfgQr1Mtqi6lP 5u5JbDpPUOCQbf6F2mujmHfSJYJvYupGo9Qu0hfGTeneUSqKfqM8TWDF81kY epvAenbm29PUFls16xz+onWSKjQIoTZOEEar/U3wW4iD8QNqvcBja3nRBOnD Mg251Ov1D+2anUCwPfTFHIkZmr90RYmGf+hcOAuj5KhVVjbyEuje8Xken6RM vXTSxu6XZwTDJfE2etTynjKKClwC2evCXnPqhU0VrV1ZBPnFL1iO1LOyTTyD 6B5pSv/M9aEW/2nWpv25BHsO6lhfpJ76u/CragH9rgDZEyHUI3/qXS0qoXtG 31HzETXhfzeOpHsirqGwOoFaYP1yvmsFQV9v5mg6dbumzn2JWgLN8ysL8qib YwYP19I9oDkZ7cGjbpyfrspppN8z9iCykrr2gpfg1GeCbm9l/XrqD/3rMnZ/ IYg5vN67mbr0tx5fOZrrvvcvl/Gp371/soPfQVCSXm7eQ533s4tYZjfBVhnX qX7qN4mrSvxpjnf0X9YaoM5WaLlpLSSo1lfqGqZ+HhRto0zoXpAxWjZGnTZi v3SQ5jTrAFPzjTrp6OIveTRnksrLpSep42tqOOE0F91OH4qnqGMNwo870bk9 sExSYob6YYalptaPObDKy/vhe6vmjf44J2d+XAT/B4fUTsw= "]]}}}, { DisplayFunction -> Identity, AspectRatio -> NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, DisplayFunction :> Identity, Frame -> {{False, False}, {False, False}}, FrameLabel -> {{None, None}, {None, None}}, FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, GridLines -> {None, None}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None}, PlotRange -> {{0, 1}, {0., 1.}}, PlotRangeClipping -> True, PlotRangePadding -> {{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks -> {Automatic, Automatic}}],FormBox[ FormBox[ TemplateBox[{"\"UpperTh168\"", "\"Reliability(iid)\"", "\"UpperTh170\""}, "LineLegend", DisplayFunction -> (FormBox[ StyleBox[ StyleBox[ PaneBox[ TagBox[ GridBox[{{ TagBox[ GridBox[{{ GraphicsBox[{{ Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], AbsoluteThickness[1.6], RGBColor[1, 0, 0]], { LineBox[{{0, 10}, {20, 10}}]}}, { Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], AbsoluteThickness[1.6], RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full, ImageSize -> {20, 10}, PlotRangePadding -> None, ImagePadding -> Automatic, BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { GraphicsBox[{{ Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 1, 0]], { LineBox[{{0, 10}, {20, 10}}]}}, { Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 1, 0]], {}}}, AspectRatio -> Full, ImageSize -> {20, 10}, PlotRangePadding -> None, ImagePadding -> Automatic, BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { GraphicsBox[{{ Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 0, 1]], { LineBox[{{0, 10}, {20, 10}}]}}, { Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 0, 1]], {}}}, AspectRatio -> Full, ImageSize -> {20, 10}, PlotRangePadding -> None, ImagePadding -> Automatic, BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, GridBoxAlignment -> { "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, AutoDelete -> False, GridBoxDividers -> { "Columns" -> {{False}}, "Rows" -> {{False}}}, GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, GridBoxSpacings -> { "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], "Grid"], Alignment -> Left, AppearanceElements -> None, ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> False], TraditionalForm]& ), InterpretationFunction :> (RowBox[{"LineLegend", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Directive", "[", RowBox[{ RowBox[{"Opacity", "[", "1.`", "]"}], ",", RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", InterpretationBox[ ButtonBox[ TooltipBox[ GraphicsBox[{{ GrayLevel[0], RectangleBox[{0, 0}]}, { GrayLevel[0], RectangleBox[{1, -1}]}, { RGBColor[1, 0, 0], RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> True, FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], FrameTicks -> None, PlotRangePadding -> None, ImageSize -> Dynamic[{ Automatic, 1.35 CurrentValue["FontCapHeight"]/ AbsoluteCurrentValue[Magnification]}]], "RGBColor[1, 0, 0]"], Appearance -> None, BaseStyle -> {}, BaselinePosition -> Baseline, DefaultBaseStyle -> {}, ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, If[ Not[ AbsoluteCurrentValue["Deployed"]], SelectionMove[Typeset`box$, All, Expression]; FrontEnd`Private`$ColorSelectorInitialAlpha = 1; FrontEnd`Private`$ColorSelectorInitialColor = RGBColor[1, 0, 0]; FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; MathLink`CallFrontEnd[ FrontEnd`AttachCell[Typeset`box$, FrontEndResource["RGBColorValueSelector"], { 0, {Left, Bottom}}, {Left, Top}, "ClosingActions" -> { "SelectionDeparture", "ParentChanged", "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> Automatic, Method -> "Preemptive"], RGBColor[1, 0, 0], Editable -> False, Selectable -> False]}], "]"}], ",", RowBox[{"Directive", "[", RowBox[{ RowBox[{"Opacity", "[", "1.`", "]"}], ",", RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", InterpretationBox[ ButtonBox[ TooltipBox[ GraphicsBox[{{ GrayLevel[0], RectangleBox[{0, 0}]}, { GrayLevel[0], RectangleBox[{1, -1}]}, { RGBColor[0, 1, 0], RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> True, FrameStyle -> RGBColor[0., 0.6666666666666666, 0.], FrameTicks -> None, PlotRangePadding -> None, ImageSize -> Dynamic[{ Automatic, 1.35 CurrentValue["FontCapHeight"]/ AbsoluteCurrentValue[Magnification]}]], "RGBColor[0, 1, 0]"], Appearance -> None, BaseStyle -> {}, BaselinePosition -> Baseline, DefaultBaseStyle -> {}, ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, If[ Not[ AbsoluteCurrentValue["Deployed"]], SelectionMove[Typeset`box$, All, Expression]; FrontEnd`Private`$ColorSelectorInitialAlpha = 1; FrontEnd`Private`$ColorSelectorInitialColor = RGBColor[0, 1, 0]; FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; MathLink`CallFrontEnd[ FrontEnd`AttachCell[Typeset`box$, FrontEndResource["RGBColorValueSelector"], { 0, {Left, Bottom}}, {Left, Top}, "ClosingActions" -> { "SelectionDeparture", "ParentChanged", "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> Automatic, Method -> "Preemptive"], RGBColor[0, 1, 0], Editable -> False, Selectable -> False]}], "]"}], ",", RowBox[{"Directive", "[", RowBox[{ RowBox[{"Opacity", "[", "1.`", "]"}], ",", RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", InterpretationBox[ ButtonBox[ TooltipBox[ GraphicsBox[{{ GrayLevel[0], RectangleBox[{0, 0}]}, { GrayLevel[0], RectangleBox[{1, -1}]}, { RGBColor[0, 0, 1], RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> True, FrameStyle -> RGBColor[0., 0., 0.6666666666666666], FrameTicks -> None, PlotRangePadding -> None, ImageSize -> Dynamic[{ Automatic, 1.35 CurrentValue["FontCapHeight"]/ AbsoluteCurrentValue[Magnification]}]], "RGBColor[0, 0, 1]"], Appearance -> None, BaseStyle -> {}, BaselinePosition -> Baseline, DefaultBaseStyle -> {}, ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, If[ Not[ AbsoluteCurrentValue["Deployed"]], SelectionMove[Typeset`box$, All, Expression]; FrontEnd`Private`$ColorSelectorInitialAlpha = 1; FrontEnd`Private`$ColorSelectorInitialColor = RGBColor[0, 0, 1]; FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; MathLink`CallFrontEnd[ FrontEnd`AttachCell[Typeset`box$, FrontEndResource["RGBColorValueSelector"], { 0, {Left, Bottom}}, {Left, Top}, "ClosingActions" -> { "SelectionDeparture", "ParentChanged", "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> Automatic, Method -> "Preemptive"], RGBColor[0, 0, 1], Editable -> False, Selectable -> False]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{#, ",", #2, ",", #3}], "}"}], ",", RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",", RowBox[{"LabelStyle", "\[Rule]", RowBox[{"{", "}"}]}], ",", RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), Editable -> True], TraditionalForm], TraditionalForm]}, "Legended", DisplayFunction->(GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"], ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> Automatic, BaselinePosition -> {1, 1}]& ), Editable->True, InterpretationFunction->(RowBox[{"Legended", "[", RowBox[{#, ",", RowBox[{"Placed", "[", RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", CellChangeTimes->{ 3.886654209613905*^9, {3.886654286611533*^9, 3.886654304186021*^9}, 3.886654474752037*^9, {3.886654610235767*^9, 3.8866546652038116`*^9}, { 3.88665472586182*^9, 3.886654731992627*^9}, {3.886819732601428*^9, 3.886819736842751*^9}, 3.887203298083955*^9, 3.918565664580105*^9, 3.918565758797106*^9, {3.918565878042244*^9, 3.9185658950717907`*^9}, 3.918565974749928*^9, 3.918652523795926*^9, {3.918652634194561*^9, 3.918652639585363*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Question 2 Reliability function and expected duration\ \>", "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}, { 3.9186525713158903`*^9, 3.91865262171565*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"dist", "=", RowBox[{"ExponentialDistribution", "[", "1", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[ScriptCapitalR]aircraft", "=", RowBox[{"ReliabilityDistribution", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"X1", "\[Or]", "X2"}], ")"}], "\[And]", RowBox[{"(", RowBox[{"X3", "\[Or]", "X4"}], ")"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"X1", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X2", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X3", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X4", ",", "dist"}], "}"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"SurvivalFunction", "[", RowBox[{"\[ScriptCapitalR]aircraft", ",", "t"}], "]"}], "\[IndentingNewLine]", RowBox[{"Mean", "[", "\[ScriptCapitalR]aircraft", "]"}]}], "Input", CellChangeTimes->{{3.886663255298806*^9, 3.886663265145617*^9}, { 3.8866633003841133`*^9, 3.886663323350614*^9}, {3.886666547619432*^9, 3.886666564208694*^9}, {3.918564822929894*^9, 3.918564829754044*^9}, { 3.918564863917988*^9, 3.9185648765419617`*^9}, {3.918567784240263*^9, 3.918567793903556*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\[Piecewise]", GridBox[{ {"1", RowBox[{"t", "<", "0"}]}, { SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[ExponentialE]", RowBox[{"-", "t"}]]}], ")"}], "2"]}], ")"}], "2"], 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->{ 3.8866633296679897`*^9, 3.88666650751689*^9, {3.88666654907437*^9, 3.88666656494932*^9}, 3.887203303425775*^9, 3.918564830662015*^9, { 3.918564868557083*^9, 3.918564877237831*^9}, {3.918567785136503*^9, 3.9185677947626657`*^9}, 3.9186526436248913`*^9}], Cell[BoxData[ FractionBox["11", "12"]], "Output", CellChangeTimes->{ 3.8866633296679897`*^9, 3.88666650751689*^9, {3.88666654907437*^9, 3.88666656494932*^9}, 3.887203303425775*^9, 3.918564830662015*^9, { 3.918564868557083*^9, 3.918564877237831*^9}, {3.918567785136503*^9, 3.9185677947626657`*^9}, 3.918652643627129*^9}] }, Open ]] }, Open ]] }, WindowSize->{913, 1295}, WindowMargins->{{Automatic, 133}, {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, 494, 7, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[1077, 31, 480, 9, 53, "Subsubsection"], Cell[CellGroupData[{ Cell[1582, 44, 6522, 201, 556, "Input"], Cell[8107, 247, 1444, 22, 218, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[9600, 275, 391, 5, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[10016, 284, 1584, 35, 97, "Input", CellID->522227289], Cell[11603, 321, 672, 16, 28, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[12324, 343, 415, 5, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[12764, 352, 137, 3, 32, "Input"], Cell[12904, 357, 266, 9, 28, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[13219, 372, 448, 6, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[13692, 382, 2453, 63, 243, "Input"], Cell[16148, 447, 650, 14, 36, "Output"], Cell[16801, 463, 514, 8, 28, "Output"], Cell[17318, 473, 517, 8, 28, "Output"], Cell[17838, 483, 512, 8, 28, "Output"], Cell[18353, 493, 28471, 532, 239, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[46873, 1031, 494, 9, 59, "Subsubsection"], Cell[CellGroupData[{ Cell[47392, 1044, 1281, 33, 97, "Input"], Cell[48676, 1079, 2050, 57, 55, "Output"], Cell[50729, 1138, 334, 6, 47, "Output"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)