(* 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[ 44528, 1008] NotebookOptionsPosition[ 43456, 965] NotebookOutlinePosition[ 43866, 983] CellTagsIndexPosition[ 43823, 980] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Reliability of a Car", "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}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Show", "[", RowBox[{"Graphics", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "10"}], ",", "0"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "6"}], ",", "0"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "0"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"2", ",", RowBox[{"-", "2"}]}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<1\>\"", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "10"}], ",", "0"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<2\>\"", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "6"}], ",", "0"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<3\>\"", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "0"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<4\>\"", ",", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<5\>\"", ",", RowBox[{"{", RowBox[{"2", ",", RowBox[{"-", "2"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "12"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "11"}], ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "9"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "7"}], ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[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]", "\[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]", "\[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]", "}"}], "]"}], "]"}]], "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}}], Cell[BoxData[ GraphicsBox[{CircleBox[{-10, 0}], CircleBox[{-6, 0}], CircleBox[{-2, 0}], CircleBox[{2, 2}], CircleBox[{2, -2}], InsetBox["\<\"1\"\>", {-10, 0}], InsetBox["\<\"2\"\>", {-6, 0}], InsetBox["\<\"3\"\>", {-2, 0}], InsetBox["\<\"4\"\>", {2, 2}], InsetBox["\<\"5\"\>", {2, -2}], LineBox[{{-12, 0}, {-11, 0}}], LineBox[{{-9, 0}, {-7, 0}}], LineBox[{{-5, 0}, {-3, 0}}], LineBox[{{-1, 0}, {0, 0}}], LineBox[{{4, 0}, {5, 0}}], LineBox[{{0, -2}, {0, 2}}], LineBox[{{4, -2}, {4, 2}}], LineBox[{{0, 2}, {1, 2}}], LineBox[{{3, 2}, {4, 2}}], LineBox[{{0, -2}, {1, -2}}], LineBox[{{3, -2}, {4, -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}}] }, Open ]] }, Open ]], Cell["MAP30#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}, {3.887203586315774*^9, 3.8872035919214087`*^9}}], Cell[CellGroupData[{ Cell["Question 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}, {3.8872035562635403`*^9, 3.887203561802981*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearAll", "[", "\"\\"", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dist", "=", RowBox[{"BernoulliDistribution", "[", "p", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[ScriptCapitalR]car", "=", RowBox[{"ReliabilityDistribution", "[", RowBox[{ RowBox[{"X1", "\[And]", "X2", "\[And]", "X3", "\[And]", RowBox[{"(", RowBox[{"X4", "\[Or]", "X5"}], ")"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"X1", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X2", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X3", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X4", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X5", ",", "dist"}], "}"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r", "[", "p_", "]"}], "=", RowBox[{"FullSimplify", "[", RowBox[{"Mean", "[", "\[ScriptCapitalR]car", "]"}], "]"}]}]}], "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}}, CellID->522227289], Cell[BoxData[ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", "p"}], ")"}]}], " ", SuperscriptBox["p", "4"]}]], "Output", CellChangeTimes->{3.8866632462219687`*^9, 3.886663327579009*^9, 3.8866664730382547`*^9, 3.886666505051875*^9, 3.886819735317889*^9, 3.88720329573217*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ SuperscriptBox["p", "4"], ",", RowBox[{"r", "[", "p", "]"}], ",", "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"}], "}"}]}]}], "]"}]], "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}}], Cell[BoxData[ TemplateBox[{GraphicsBox[{{{}, {}, { Directive[ Opacity[1.], AbsoluteThickness[1.6], RGBColor[1, 0, 0]], LineBox[CompressedData[" 1:eJwVl2cgF34DxEVJJUopshpGKSojEt+jhGSUUWaZZWWUiGQUkr1SVkgkUUZl 7529JVnZ4VdWyR9Pz6t7dZ+7F/fmDhjZqJlSU1FRaW+govq/KppOtJZOapLT T4+7efL4nx5/d8VogFUEocot+p0zNFJ7tnUGZrPKwqFidyjfzDmpvGJXK0de FfwYFKzsEzOXEjy9OymWVQMWCkPpLdOPpKh2TYatc2lDNPiDl5vac6nW6aKH hrzX8FWDzT5M7I3UZeO6XMMIQ3jrdT/o0s2RkmgRzghlNYEmu5Bk0nSF1CGp F68rYm7gsfLVTLGpZin6VLq4BS5zuKhWsmiq9Ugt7LkTwZNoCf7xlLLlxiGp b4++BVzhtYa1u3KDtdiklPGfxPIKDVvQ5jA25uv/kuoW1CZ6EXZgZ1M2ztP9 LaVkypC/0H0bHh9vNx6oXZMqja4QDWC1hyf/3UdB0zREpO1eJo/uXUiML59Q MtlC3tAJChTHOEDUta2CZYqRcOJ7ypV+R/TY/I1Va95FQu8+56ZwOeHmusEw 1FgIbZpy/GNDZ/ROPNTZGsxBnIep2fcn3oduR1Hij8YDZJYl91nuiAtcORnc v8nyEGPVW7su87oiNPTuPT2xI6TH62DQ5E03MJxkajLMECC8/ZabyjTcEaxv zfte/yQxcJI7F7DoDh3tDh4OIREStfuAh3aEByDA1JWqK0Y63q8U84g9BEXH aqZiUIIwXOz671f3Q7hUho8z1hKiMJYhUXzvEfivdFKf9pchjzz87vmyeiJZ h+O15/Q5Usx+49OVfE+ct4uTe+4jR/7kSC8c1PVCzUVGfphcIELqbEKUFS8c Uup2MXqkRKxmF20KYrzh7MmivGVKlSQ/aUl/LPUYwbqd5481XSaD3G9/qPc/ huJRBu8LzepEQ9fg5jTXE9z0E5EXVdMigUsSSbmlT1Ah56QW0qNDakOYv3sa +sKGQW/XWpA+oRb4uf8ytR92WZzqvCNlQKRqP1/jSPRDr219+EijIblnnBQz ec4fblY7FCOcjUnWmlvvxxF//Kd9xaZT1pTwiopeUeENRL5OgIq6mDkxaGEM 31cTiJOVnlqXjCxJtOVU69jNICzVP7l9NeMWoWttTi7RCMbL71zqb/TtSBJn URVPUjAyxbMs4otuk7NWqSN+i8Fw3FUSt0fInrhs9jqoFRGCLeccgxJ1HQmr 5m2Z4rEQKB4KE9NkciKfXl434BYLxan4rT0Fg87kp5TEi5/doZDPS1mgrXUl AX58RVcOh+GJwv39anbuhP/L7r7Ce2GwIr+ZRPw9iIk9hfUJazh+s8+Lu00/ IsI0oc5ZtuHwu5T094+KF6EOFfn6tSYcT4vivGMqvEnce6cYQYensHF3v9wx +oRYE/bVq41PIb83Pz0l3I9INhbre3BHINp8mIFPK4D0TtFwdbRFwGn3YTIQ FExSnJLdVo88w40uGp6I0BDiSHdhkNfjGf7S1zUvxYeS3byBCU7Hn+PngavG LMPhRNWQhZvLPxK83wYNvqxHEs6f+Z4K3yMRkBsp1WYeTaZd9UftJKIwl+Oi rDccQ3xjXiZXTkRBiD5xvxZVPNE6en7zLKLRNrylOKE9nvDlj9/c+ywamXtn Lq6+SyCV3ceOWJyPwZCHc0q+ayIJu9H8JCwmBnVM8Re977wiRot2U4XzMdiX J+4jZpdE1ply3jK+jEVsBHcQj89rIqEiI/hx7QVIaZWkKn8aofv2PbBfMw5x Zi7BRlbppNvSm7I5PQ7+nWVVB/LekfxKU610gXhUhUjG1uVlkIP0OXRnteOh XFpsMmCbSZ6o0+V1ecZjZ2OUVaVAFtEaTmWl6osHq+JhVqe8bFJy5L+68M0J 2NHO+/exzwfCa6fsfEQ4AQWWrOEj+h/J4jqlV803AdcUU3/TseeQUA7RmCTx l9A4Wv7uxWQ++WvirSRh8hL0Mh/l8mYLiGFa939NQS9RMDlOI7hSSE6ccdb/ M/YSIt+mZLP4S0ijVgnnxaeJqFcPOLx5oYyIxO9oHihNxK3Dpvt/Pi0nMeOG bvbTieCZ35m9R7KCWDhsHIw99wqfww1Xbz6tJHThFxJ+/nqFkbQJF2HXGrIi PrSSsC8JL4WYI/tO1ZLZb/euqJ9Lgnl4K33xfC1p50vZ9ik8CY09g3aWzp/J iwJah/tiybj/nqIqU9RIQgxetBwzSEZzko/Fg8gm4rnp1NF+n2TMF1z/6+jc TMxVTQele5PR6m8565DUQkS+VyjSPniNLcwNcSNhbYTPRzcpJ+k1NjiH6c8x t5N9AvPrZk2vsXHpz6XkqHay7nDwYz1XCtoDT7vzpHWQz1s9uELKU/Aq/c5G r59dxECILLDRpeJ+iAVh39xH1Ls7VRpPpKLfe+7uck4fkXO59cZVOxXXLwfG 7rH6Ro5Wx1wbSk3Fv1VeOt3fT5a0V2qTld/Cl2rXYNziIJlcCz2k5fAWsX9y y2J1h0hfIr/rlri3yDnFvWJSMUTKZrSFrX6+RRHnqXyT58PE3yM39mRYGqrl ttKUao0QN95Lf4YL0nBoMmtTXOMIuV0/rhY+koYXXD8/3pYdJVeZ99L9Fk0H VR/HdQbxMXLwzd3bhT3pUKVXvfhBbILktAjJy3O+h9LUzg2lsdMkcHJa4Zjc e0Te1bgXdXKG3KB+rbjT+j0GF89Sv6+ZIXtE2FS+Fr1HM91jjti/s6Sg3iM1 RzADhwJitfcW/yRsxy0yLzZloECg6tkrp3nifUZeiAxnQPIl547SrnkyJ8+d fWIpAwqq0x18ogvks0H/B2bOTNyrdAubWFwgzqFquQO3MnG/LbvP6/ES6V2U KLmzPQtiN8Nk52eWiRw1i/SNA1mYF/6ppWT4l2QxLJZqiWZBrss7hrvrL/Hl e18upZ+F2ZGxieuVK0RC+1D15vQsDNfQjF3LXiWRhdsao5WyoWKw3VyCQoWN dRPKgQbZ8FnnsE4V3QDbzqomd/tsRG2mVlp02QCFWbcW05hsFA2vJBxkoMYf roX249PZGKUV8t1+hgZaj/p6K/w+YMM72y+5pZuwY5D32M2ED2DcnlQ3zU6L Okm7B1tzPmCb5I8EWWdaSCxt2n95+AP0F10SzcU3g838uGm/+Edsbx161VBO h36Vh5Q/ox/Bdkg/nZ2JHhFvG6RjVj6CuyFZ/IMHPVTp9oZi5yfcmDkn9GyO HqVlb0W8JT+B6kvXmws925Eg0um0K+wTZF/a1KZkM8Jk3+GNgtI5OFge66jU tRPsjrc1WzVzsOpwMomRlQmd7YXJ9pY5+GJ6LDBAjwlyAZcvFETkQEBSZb14 lAl8VPcDFWZyIM0mGce5YTemRhtZjKNyQXX89Aqt/h7YZN4ReL6Qh9Cv347Y ZLNhVnKovY4uH/VVTYJbtrLDqlbFeYU9Hx1qLq9uGbLDbOBIzbXz+djEx9EY xcQBg+2DBjwR+ZijFvyU4sqJS+ZK4VliBUjkUQ3ULNmPpoU8iZGLBXj2uaJH +td+KLnzDTEbFCCNd9ws+tABKDyjFnTyKYD/PtHZ+CcHIF2VW4MvBWDTtM1e 1zmIEwd4VhqcC6E2xTn9Yhc33qWFJqwFFsLShnm0QYkbx8SpFE4kFkKnpjvV 3psbh1W/hofVF8JdWFBVZIUb+x+ECOqwF8Eg7vOS9xQPdn5ZNRwvKsLWwHeC u4b4MBfcVbthQwmu6W9MfCt0DIVWmRjZU4JNkvElsQ+P4bGC/6fqYyU40VZv dLr9GNipzr7y0yqBSKj9sq2DAM7bpLsxZ5TA11/q40qlIBp4z0aHHy/FrprC lTdlJ5AZ/r7LS6IUirmLy3yUE4ig5mByPF+K9OB6HWqOkzDs/+2jrVuKHIU4 sSank1h6mu7A+fif/4j73hYxIezfxKqW0l+Kzjdhl35UCWPTHe+AyMlS3Hff lmqxLIypwfla34VSsH26q60iIIKPhU24tbUMdG9vl8tGiEDR3lNA6FQZQhtS tvxnJQr77xS6woAycPc6jm4WFENtWXVJs2Q5rn+Ua5GhPoPkhv9GAuTLYXSm wYTj7Bl4dQttVVIrh87y2Jz5wzM4O/NCo/ZmOSzMZhm1NkqikMVxsjS0HC+u dk9FbJdChg3frqyJcszlf9jBfAp4zuFzIzy8AquZJjLmv2TgcLjYTy2uAmmP PI2mWM5CU3ghY0dqBX4XskanSZ8F0wWDFf+SCrTuPGG7GHwW/vbiwV5TFahg vOkRL3IO7vUTeQ7SlZg698052kcW5k4XtmtPVyIuzSKB11QeqWw79a8tVeLY 2y4jllB5TBf1pBlTVcG3bmONYok8rKnNlKx3V+G32XGb2/sUYO/n7fdIsgpd odNbOtoV4BZbseWdfxUcOm4e2quuiKdlUrQ0AtVQEb1Uq+WljC7jTVfoxKpx imZmsSdfGSy0jUnbZaqhMfc1P+GnMqIU9c6zaFajwGZ1B4O+CuLbnT0FHlTD u3Vov/ZpVbwdzaHWaqxGyJCO0bLbJZRtEVpPu1UDn0eNPzyN1XBY40SO770a NFtv35HvpYbgF4I2Zo9q8N+B1W7OFDUYCB8dOBRZg6v7omjuzahhTY+7JKqy BmKemxJvOatDImOPmw9bLeazHjAGxGrgw5WVNeO6WvhunhX9suUq2BOWP8l0 1EKq49KYttBVPPrx25proBZWX8rHGHWvQs19ob93oRayn3JD2dOv4uebmeLL ++tQbRufU6SuBYHVAVc41mE8cLOrwlttJCdWru3j+QxLh+DbTZ56sPXSGMLx z3hQRDPJn6mHMzdHKkxOfwYXw3H6gm96aOHf+OSd8mdse0Cz7CCmj+XMc7vO OnwGNZ1Bm+GMPpRKy/nMaz5juCtjhNf4Oub7Si/lmNfj2zm+a9VnDFFcfEm4 7049eoS4G65oGsInfpB5g2s9QuNi4mlsDMFuQvVVMbQeXu7bWrNeGkLuB0z7 8+vhGzYSa77NCFHLxU6b6Bsghx12F4eNIL2n6KX6uwZwk97Bu8km2PiU2eZ8 bgP6WWxSD1eYoHaX9Rmx8gYoPxNTXx4wgepOro59XQ1o1BJ/usBqimv0HpuG VxsQTq23XzPIFPepz5vZKjfilHfV0xa3G/g02yAQMN2IFLHVJ7L3zOB8i+ev 61IjRvVtB78+NwOZflBtS9WEm56m+WF5ZqiaFLyusbsJZ3yharpiho6R4GA2 ySZUvOTTDXU3x1yvxvwbvyYkyc/R8oVYQKCmL7eavxlTr9rcOuqtsGfWciZY tBmcVN1BdfNWoGJeOaAr3Qz+6FLeCbZb6DBi9aNoNmPrTUm9l1a34LKmqc/i 0YwSjhZ6hh3WaBBt3mDR3YyXe+v6vl6zgWibQRLt2RZEWLNRBzHYoUNaffbN bAu2nizNMtxpj79x32Oz5lsgnCebfuGIPQ6s31Eu+NOCr68ur8rJ2MO6KDyt gboVqc7FLR529tgs0WVB2dMK+fj6lOU2e0gIa4+LoBVS2goXViPvIp7n+mBJ UCsit/259U7cEVZbLds6T7Rh1X1fxtMCZyQX7fmkeKoNKbyyLjlfnTFgWx5Z cqYND7y5xJZWnKHWzWr4Rq4NFtAo/ix5H+Kvaikuem3I2/hpubXkPjYS3u3c Pm2IeW1+y6zeBTF2Q/K3B9rwYmNRwollV9T3XC1iCGyHJZXJloAvHnjYO85s EdaO+iD5I9wzHhDvc7Suet4OCn+fST3VQ7waeMblktgOycPGaoqH//3osW6P ydx2DLU4rW299xACC1flKr+340Cn9PW4fY8QxKjV7HS6AypHw0fVrDyhLqc1 NDLSAYnhd9TD5x4jf9fJ5u+THRBed5Ti13mMg0NbioZnO7AnqPPuQ9vHmLtf 8HzwTwdqbg+vGsX++9GZnJf66Dvx2iJXZvT3YzSwjxa3i3TiMvPK5cX3PpCd t4sp9+yE65neMqdjvv9+pt/VeO4u/BqeOFevFYCMMjenbfxdcFNysgu6G4Cj 3+9EOxzvQh5/UYlZaAD28+oNKEl0gXYxd1ynIQDb0o7dXFbtwpFVj8dEJhCD OY0Oave78IA5nZP+eBD8mhkjNrZ1IcPy4rJnQDAG18I6zNy6sZ2lRtsuOhSj F5oT91T0YEfy58E7cxHIiBxwaj3Qi1mGzDtODjFI8qF5csT5K+j6MCBnmoBF Y52pGwV9eLrNtkGs4RW2yXqrZe7tx9d1DqMw2jdw2TFKP6Q3gJ6hdsMS73TQ Fx+l6lYehFP26g5t6UxIOaiuVvwdhBILi+Wa4gfEvPJPPBQzhL/hlN77zjm4 pinSuOXiMC7c8tX9caUAHztNw4qXhqE7wyhLwkpwuiGDeiziO5ZW0pKmlsuw //yNxTDZEYhLbeC6FFkJURHRkA9jI2CwuqewcLEGA3MBdYleo3iReDis7MRn TAtf9mIVGkO1enCxU3wjeH8ITG1oH4PIxeCjJsEtqOS+22brMY6/LVYyQwlt COroNFbjnkB+w6Y76QUdoKiXhlBXTkB85HZs/2IXsjSZz522m8RH1Y5Z2rAv SGx8FDvMNIWKBYf+BNE+/K7Ru89UPoUZ353TvIoDGAwpWdxh/QP7ujlv5MkN Yan1DOtDhmnITrgMrU0Mwzb8YKlT4TRCfukUqDePYG/jwR0j12bA1eLFFvVx DOqdaf+xr83gmMx83ETmBOauJ1j1pc5i/EXT+ytrUygxeO/FoETBitRk93P5 GeQ3W13sV6GgKimxgkttBp8I/853lymwd23weqM3gzT2pBjlqxTU+d4JqrKb QVRPVLa/EQWMvderuWJmcPeS99BWJwps93GK6v+awVFpfanNyRRs9Fp7ux47 C973+2i6UygYs5I2Hk6ZxUHOntrktxQ4X7u6oTZ7Fiz/qWnIZf7jn929EF03 C9pcBUuvQgr0vp0pv7E4i6HjIpE07RSonPpt76NMQd+LX9faOymIzHHtjtSi oGf7e+7EHgoMD+4/8s6YgqYfRzLO9lOg410RPfCvV+FrrhqPSQoiupgaTf/1 yt3zzf/yNAUs8ZRPgf9ys72i1A5QKKjn2x6e/y831Zi5v3SBgtZ8Tn62f7lJ bW2Jwb8pmNnMMaL6jxsvE2xu8JeClgjbsMf/uDEZysdPrP7jJL0QL//ne8a1 bXF9nYI7rsc6/q//A6NkeDQ= "]]}, { Directive[ Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 1, 0]], LineBox[CompressedData[" 1:eJwVjWcgFX4Dha0ymgpRMkPLyErK72iQmS1KurISIURIIiORrFSSjCijSGau nZE9I9lkcxu0SO///XQ+nHOeR/CCk741Ax0dnTo9Hd3/U8N6qr1i2og0rjX3 ChCJPzT5yvjCEI8s1rZksm+Y36rEta47/A3PCdSF9rE9mDVQKi674eAhegpJ 7kcdx2U9lSQOcaQ+4THEiJR3TvZ0tBLd1unof/ym8Npx1LBY+4VS+1ypv4Wo OSyufRhIPlCspGf5vsgi1gIV9xfl7I3qlBTbZHKieKygu8FN33KiU0lYKeF5 dbwNfM4X038dHFJan8HydJHfDiFc2Q31alNKi1yusSIp9gjcRzzVa78qDdwa uGss6gj/CNP8u/t+K1n+SqmqNnTGadYLtAFDetIjYUrMYq9gUCBocvQUM9Gy 3vh2sccF7zZY3qAv2EgqHlfL3eVxQ/Jm5sp1w1uJbMe11yJnr+Kgdu+6MwY8 JJ1FQrws3h35AlO+oZ38hA9jL4wHPVBAl/YjtEKYRF19uIvG74laIZazYthN 1mZpJwZbeMFHQUIh00OceI0y8AqkeCNvWEQotOwAWeAuelA0fh3Nm8cU0g/I EUudy1v1RG9A0UqYEsd/iPQGCt2btvVFdeZEEIlWIqKD9msqDW/CyOWL55Lm UULxVD1+d+km2NPot+XzniBxHIJ+prF+sCj2//b36EnSlb1cJnLQH7NiPx32 VmmQjZofVr72+ONKRotla8opojaRo1h27RaUh7u2DLrrkVt+odfu8ARgx04d GZ9OA1LGa1Ng/DYAs8NK223tjcmvQuVFobOBaJS+vXTmmCmRNtghTVsORHaE PIecmRlxWFhyKokPgqzs/eEF6nmSFtL2MlgpGFX79l3WybMgw7syZw0Gg7FV 6Ywa9bUlMTxLsZ3jD0GLqaE20/6LJPyHYmpRRQi21ddHnX15idRHco4FWNxB XAXdFM5fJgziXwT0GEJxK66wjlXImSjVN5jvTAmFANPHROHsK+SaZWr89PEw uD7U4xQ3cSW5q759+eNh6JqX/e7Ad5WIyskZnxINR13KDZlWZk9CadsUs70u HKoGcUop4t7ksf1M+4TtPYgExP/d7O5DWNpb08oNI9B9lZ5VXtGPpPKV1oik RkDgr4FGcqw/OeaQMR66FAEiYRmtyhxArjMHCpnERiKmw7hffXcw4TFyOVo2 EYmXIXv5D/fdJgXJ5ym7DkbhMaPQwu2UO+SLkmLCl54oCGVfZQ7yDSd3Q8VK jXdHYyU4jOObegTZ+5Gjn3otGhmRy0dvWEQSKzcaTwhPDPgjrS44v40mMoxR XrnOMZCyOHA+mPs+YYiS/fSpLga8K4ONXrdjydNsz3gJ9/sIadJwOpP4iDgS 3r+nm+/jm4W8/w31x+RIc9k5v12xCLE+QV1Y+4T0zTDyd3XEglvOTeApJZG8 8Ezz/bvnAR5Tj3vmnU8iHizqw6J+D0C3LKB1+FIy4RANT/KUfIj2S2b7fyQ/ IzoW3Lv4wx5BUpXeoyMrnfB9eRugNvYI1y47FPOyZ5K5G+c+X1GMw/TBvU/S b2WRO/HJae+m4vCYu3WA7X42MdmnwryAx7B1mWTSi8shYm8nbbc9eIwf3JZv 6Vxek3c9+/dcUonHqq3T9+5Db0i0TWtIdHw8Ht17nW2xN49cWLoyQ/0ejyaJ sJUnwvnk35bCzE3JT6BSMWewLFVIFE8dlchfTYDcz8sfJEtLCMvAWPig0VPo bbxYIfSbSnrsg2jML5/CxIg27I0y8vadtclL8URMBn7wEHavIELrC1mOmSai b6CrMHZPJQkxYCn+EJCI5Bnqs9ejlcRkNIOHrj8Rl7OVzxrbVJPyPSvvY5iT wCgf0sx74B0RvaLttUcmCdyzX5WYGGrI0j9an/6dJAyVvMjMLaglUTvl4lMV klFmVXV8rVMD+WMVpKVolYxFteqdmo6NxCKrZ6XlXjKqnnjWvHZrIlKHvc79 mkhGQ4nX9UsPWkizSTmf5v0UZAWZfBeMbyeyiZtbhypSYLahv0xMsYPET1r4 us2loG+5TUmtv4NccmcafnL8GZxHPBgExbsIS4x60pevz1CWHOUvydhDlhVG lpO2p+J4ZpXpjsIesjBwzdjgeCqchvwctjv1kk6xF+sKYlJhekL2dMTsR5JQ stbd+2Aano+HTW3lHiCRlIS2/ZQ0tDnsvqG3MEAC1sjvG7ydBmUziVOC7weJ nY71sHJfGgZlfR6aqQ4T2bFqjbU+z7E73SCqWXSUiN0+m1qY+hyldZfcd6aO ku3i3/9dbHkOt5rYq79Fxsg/d6H8Rv4XaGfS1romOU4a2Pz4I6teIH/nKEfQ hQlCkSaLO1gyULNMlc3XnSUGPd2nmqUyYJtSSGjLs0T1+uX0G6YZIKuzlSoZ c2Rfbbz5SEYGMoMD9ztuXiA/TJfr07QzwWPq+7Lf7wuZXo0SNnHPxJYH+Y1X xr+Q/pS9N1ifZmJ6m1NbidpXUjlvKuPwJRNrZXMs/bm+kTC/oicHorPAwMPI alP3nfiK6v4aLcnCoTyDWxIKi8SlcVI/ZjwLVlktyl0Zi+Q05zaWn3Iv4eK0 LNN0f4kIpV91ofa+RC2X/GG6Wz9JYZv0yZN82ajct9IpUL5Mwqfn1ParZkOk aWbMVHuF2DA812B3zIY9puhzBlYIl+yOU59Ks2HrPedRz7RKShr9MgolclAy KB3yVJ4OOyQvvdZsyYFZBTVxtZsBQYdPSpPRHJhGjX5SkWTEt5O73kj9yIH2 0FaBuhBGNFAG8zj5XiP8vffGW8eY4BWlXzR0+TU6D5UqSFWvQd+SYrnrhlyo xX7SmWRkhSoDt7KNYC7yLuXx73ZhRe7GpQoTuVxMu+r6tY+w4o5YdpXSuVzE pnxgulTDBkVT4Vrml7loKpihY05Yj0fUdc2Ptd5A3PEkR7vmZjC9n9IOp7yB RHRU1Xz4Zjh317TcdHsDTUqrd0/HZqgt+LZZx7+ByKOTrtzn2PGLf7FTcu4N fhVdCfTx3gKTW/191aF5kLWPuH50hAObh0X32yblwc76/kqHAifeH7niw1aY hzCGfQ1ukZxQ/LFGQG80D862Dxe+qnBhh52k9aBCPlzZLaQ2Ubdh8JQ/7dfn fLx9H1hRNbgdsZlNyvHL+fiTbrqOorYDOizbosBegNrK3+sPvNmBispM2aAj BQhxO2zoEcaLJNluz63RBZg9J0a6tflgtX03k4RyIaROqj+jrRUEr4eLUbtR IeKL50YmVATR3UlNc7MvhM7pysw7gYJQvaunXhJbCCab47n9a4UgRucdrjZf iNDaV1ZN7MKY+dzMbRlXBFuqqsmcugicXruKP1wsRiBbgs8Xzb1YODLS+Z7l 7X+eMr91T/bCof6U1zLvW8RLPGwZWtiLi0N76sxV/utv8t4titkHyoZhikjs W+gwxbSqTe+Hrp1WTO7BEkir+Gj1FkiiZbFYcVyzBDFnlljWsElB66bYCCel BDnfDp9iPCQFtQcMEp63S7BlndYR6YdSUK4pqsPHEtRMlJnZnT0AKUGR5SYv KhYisgJKlqTxKisqaTWcivCdhzQX9spgvwKdmlQKFRzUgdB7FBns1vkUE91I hf4ey2b+ZhkI+ERKnOEtxfVE+eTgTFmwf/xrMVlaijXNxgq/fOTxLeJDPT19 OSQ+iK4P81EE1eE1xrnKEfaIZdixThHBamEFtfvLQdduv2WG/TB46Y49CzUp h2BJZ2nWi8NQcXrpy5lTjio7H3fPgSNoEj32OEayAjwtp8XGrQCBNTz6LwYr INWi/Nv02jGscQ26+2i6AlttFRninh/DzPD3+juLFTh3ZMFQpucY8qktuMxW CctoaojrwePQcAsQl5avxHHOKl75leNwG6OxUO9WQjfsxKrwAxXUV9aWtx6p gskG0dJXnOpIa1oZv3uyCv/mqkZ6ddQR2CPNpqVfhcWZLeE2d9RxbD7BsN62 CnsTiqVf0WmAyu0xXRFVBWbpqPQ/XzWQ4yS2NXeqCst2N/unJrXwcOdtm5iY avh+oHlyROnCfXdZqP7TajhcqXnZnK8LI5nFnM0Z1ZDcp/Oi/KMutqhTlsPK q/Hb/UjvKSE9hLkpRATOVCNhcs5DoEAPNxunit2V30FcNuBF9ZQ+7DzVN5jO vUOdctuhNG8jZOxgP2f+4x349K7Z/ksxwlxpb5YlXQ3qe19ZRzQZwZHhopYj Rw0WmCIfnuEzhltoUOitIzWgqlxXuv/OGL5PqllfhdVgTNJ8smWHCe5XKq1l FK8FT7vcudwfZ/DBco0xy8FayCSbytqIngX32ubUDUdrEaQrIGxifBZxGmYq 3Ea10Mmc4vhZcBaJnV4B4j61oAhrzYh6myHzcyGDSXMtStzZ47w3maOSVfpf 1uU6kIRO8Td5FOw2lCq8c60OVJ0NiX87KIhIkHC6eKsOAWw2js5fKaDI7BsS flQHsdT7z1slLLBqtqs87l0dFneRk9cyLaCYw+V7e0c9/pxRVIzIuoA84+VV y/f12LkctbO5xQq8Sb8LjnbVw/nkdLv1Nyvcmv3pyD9UD8nP/Ar7uKyhf3Nx sG+xHneu5z4/Ym6NL+nzZXoC7yGw8fSizxdriP8dugGP9xBNFr38aKct0lLe rW4XaYDgA4WTko/t4BxoOALJBth1PxkYrrTDYdvxaqtDDfjU+1CvdMoObXuZ Ql5pN+CpfJz6T/lL+P36+NZj7g24Ge5R5tJ9CVoVVWJ2dQ0Q25/zO2m7A773 V+gW2jVCltNKPL/WEWVlujL9ro3oOPykceWbI24nDnPS32iEnsr8Jld+J/Ba 0X3SiGqEgnHTmrlrTlCdhfXg20bMil7zZ93mjLjfZZ5r1jfBLK1K/EWbM5S5 SpMNXjWho4SN54CxC5juczqpFDUheeei7qCjC+q3Oh4+WNUEJ3W5jpRgF+iw 83dt/9CEwjD9OY9iF5iv91sz+rcJgyKvBVT5XOHNoHLRWbsZGX3LScFzrihY aBK/O9cM+d67F1nir8LrssifGz+a4T3kNvKp8CrInE+tM10L0jQPBL3vvIqa aYnzhhwt8G44EfF9nTu6xiMidhxpgYmTnEGAjzu+9Rl+Tw9tQVH1AF2atQfE 6/qLave24qAn628jDU9wLdjPR8i14thUvoacgyfoOJcFzyq3onbuyBu5cE90 XeAJpRm1QnW5nDuuwxPXV43Ocfu1okKu0Pq7mRea5FrpL/W0QjdgIua3hzfk Oiipa4+14TpXjddInQ+6lA0W0hfa4ObsFNRg54c/T8ee5H5vQ6+S2/dSHz8I /nPVLvnVhmNaPnRVkX5wLI3JamJoR21ZEO9KsR+YFT9conG1Y6pHTOPQOn8o yphOyqIdUu1q84M5/kgUOT9cfq8def5ygltZA+DAZt/RLdUBrZAdKfS0IKSV chVoyHdAfFRU9zJrMIacqx6VH+5AG9+NTTThYOj38Fikq3agaVP1V1nTYCg8 q6ddN+vA14EBn8Z3wWAioht23e4A+8ykv3jibcRfGTnpMtQBvqgvdBwX76Cx 93TpxvBOcGZl2nwm4fDvm+S8FN2JPfYmUg/Mw6HQ7+FY87ATlarSy5Qb4Xg2 9ID/ekonPl6hqzhSFo7rEz1+00WdELqneZAL9yC+eFr13VgnfobLy70UisC9 TSatnoe6ECilo6IoHQkDVZOR8fEu9HW2iGd5REM+MfR04q4POKJL/1BI5SGG V6O7Lvr2YPTsD+ZliwR8Vm9N4aruRYb5lhIm/2TkPBrybBfsw5KS0YuxtDSk 3mYM2eP1CWPruX2f6mdiyfLMjE1JP+IpFwK5BXOw7kSQ/uttgzi4xe6vza43 uL758/oRsyFwmJedyNEowPqyfXQ92sNIzyztCy8ohpK7zt/qP8NYaTzn6tFe ivhnYSnC8SNYoJ80yGSqhLmRbDOr5ih8zmznsw+qRn63dXTZj1HcvEOt5lao xaGmHIaJ2DFQpdRPvvxWDwEVm6XoE+PwExAQShdtgpysXGTexDiy8yb9vSit GPp2931K4GcsHP+az36hHXMyeoE80hNIlQnN5zvTCdFZ8Rn6zgk8o3y30dDt xrtdVzuc/SYRQ31mzBbTg3td3Zb6u6bAcZBNc3PnR9AMKiIZ3k0h/LCpZ65o P3KNOI8fujKNAFEu3zdtg0hpvvVkdMsMGprKhAMLh/Gzzsx7S9UMKhmZtEXk RjEcWb602XEW6owl3GfKxvCj/TCP/8Y5dLDmz4UqfYZzjFCFJ3UOnSHffmct TGBbs9DmcfN5TK6uU1aPnoJBd9YK7+o8sn07pr3JDL6dT3Loz1iACfum1e18 cyinZAdu1KJBootBg8zN422rg+bgKRr6Tbw/OyzOo4DsZX+lRwOzs+rd+JV5 ZPGmxmufpiFHZpbu3/oFxPXGvQm7QMN8PrNLm/gCruoGjbB50uClOXoy1WkB +5TPKTGn0aAy27iTc3EBotnbGXte0PBzTrTNamUBQny99WmZNAjYawTnM9HA vaJvqPqaBuOELwxnOGlYW6RmH0il4ebjvt3Z8jSMSMo+YuykoVik+GfIf57+ hK/mnd007P5G93Haj4beDdm7UnppuBzOXaJxh4aW2T05xwZp+KyRd3PTYxqo z/nr/KZpUK70Y0v9j1vENRCmN0dD5vz+2fU1NLwJjNMXpNEgFJzQcLWZhgxL zsGKRRr8C5sDNP7jpHZ0pET8pOGLHvP5ggkaEo9G2FH+0GBP+Scv/N8vPkdb UuovDZvvuq6P/G/3gH/d0r9/NDSZCw79P/8HAmndcw== "]]}, { Directive[ Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 0, 1]], LineBox[CompressedData[" 1:eJxFxXss1AEcAPDDVnlOltPPjOiyYWKcNhWpRNJV7oiaZF7LKFq0rtqadJY8 IlbRaXROJXMnKpXH4eZUdJw7brrunM77cjHHZh7VH77fPz77OMal0RMNSSQS 7Z//n0icGhBMR/hvPll/Nk5FUA9tTjaVFTYSgfBe3x3cCiIc3t/vzX9EJMCC Z10+BUQGnJ2Vd+MBcQ9OyNARuUQpvK00pOrPfDX8od8rONieB0dlK0a68prg tIZr7k8XP8ILRUM9BgbtcE9Hd7v4YCeczAwxP6cVwh3GXht1l0VwDUe4brvn KxxAbn3BqO+F3UWK5m5XMSwNYMy9nuuHU01SJDJPCfxNHtlqUTgIM4Ki1BqN FN5XmRdZSRmCR9dLpJfuDMPjIWIOuUsO88tUzAHHEZh73yjX5eYPWB9/fibp swI2DcyhN9go4duW42bqaBVs1uZGGqaNwn7XT691reDs6nzObrYajomg9hmH jsHvZIklbUu4by/fcOLxL3jXsSR9SaAG9qH6FDdN4KqFgi8c1jis9Q5jEV4T sPOs+4zBIC6kZErSsybhh1JZPJ0yBesYgmJDIf42wvqo79VpmNOXXTFmNQMv i6JvWXXio8Xtessrs/DSwAHiroUWTi91EjBbcJs+J0tNzG+YIatbtVvHFy5W pSpq5+D2WB7L4qQO/iRODVWewt/7u26vD8Pr7LhsWiReLi9vzI/DM8/kqE2Y uFvABb+tNbgzz9Zo+BXuZC/vqXmD71ylhwc14Fuaj6ewWnC1B7XMaBBXPJ+P GZThcnMehSPHv8+68I8o8ZaXDqKsabyZ/DM/TIs3ssrpjjq8Nt5aKVjEuRIJ p2gZrzxclBy7grP5NA/PNfyJg6l+YwP/CxUIhds= "]]}}}, { 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., 0.9999999795918367}}, PlotRangeClipping -> True, PlotRangePadding -> {{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks -> {Automatic, Automatic}}],FormBox[ FormBox[ TemplateBox[{ "\"UpperMinMax\"", "\"Reliability(iid)\"", "\"LowerMinMax\""}, "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}] }, Open ]] }, Open ]], Cell[CellGroupData[{ 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}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"dist", "=", RowBox[{"ExponentialDistribution", "[", "\[Lambda]", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[ScriptCapitalR]car", "=", RowBox[{"ReliabilityDistribution", "[", RowBox[{ RowBox[{"X1", "\[And]", "X2", "\[And]", "X3", "\[And]", RowBox[{"(", RowBox[{"X4", "\[Or]", "X5"}], ")"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"X1", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X2", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X3", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X4", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X5", ",", "dist"}], "}"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"FullSimplify", "[", RowBox[{"SurvivalFunction", "[", RowBox[{"\[ScriptCapitalR]car", ",", "t"}], "]"}], "]"}], "\[IndentingNewLine]", RowBox[{"Mean", "[", "\[ScriptCapitalR]car", "]"}]}], "Input", CellChangeTimes->{{3.886663255298806*^9, 3.886663265145617*^9}, { 3.8866633003841133`*^9, 3.886663323350614*^9}, {3.886666547619432*^9, 3.886666564208694*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\[Piecewise]", GridBox[{ {"1", RowBox[{"t", "<", "0"}]}, { RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "5"}], " ", "t", " ", "\[Lambda]"}]], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"t", " ", "\[Lambda]"}]]}]}], ")"}]}], 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}], Cell[BoxData[ FractionBox["3", RowBox[{"10", " ", "\[Lambda]"}]]], "Output", CellChangeTimes->{ 3.8866633296679897`*^9, 3.88666650751689*^9, {3.88666654907437*^9, 3.88666656494932*^9}, 3.8872033034341717`*^9}] }, Open ]] }, Open ]] }, WindowSize->{808, 911}, WindowMargins->{{Automatic, 302}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, FrontEndVersion->"10.3 for Mac OS X x86 (32-bit, 64-bit Kernel) (October 9, \ 2015)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 355, 5, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[960, 31, 5313, 165, 471, "Input"], Cell[6276, 198, 1085, 17, 151, "Output"] }, Open ]] }, Open ]], Cell[7388, 219, 390, 5, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[7803, 228, 393, 5, 29, "Subsubsection"], Cell[CellGroupData[{ Cell[8221, 237, 1316, 34, 97, "Input", CellID->522227289], Cell[9540, 273, 323, 9, 32, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[9900, 287, 1089, 25, 74, "Input"], Cell[10992, 314, 28542, 534, 239, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[39583, 854, 393, 5, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[40001, 863, 1211, 32, 97, "Input"], Cell[41215, 897, 1990, 57, 53, "Output"], Cell[43208, 956, 220, 5, 48, "Output"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)