(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 11.3' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     10906,        321]
NotebookOptionsPosition[      9542,        287]
NotebookOutlinePosition[      9927,        304]
CellTagsIndexPosition[      9884,        301]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["\:8fb9\:7f18\:5bc6\:5ea6\:51fd\:6570", "Section",
 CellChangeTimes->{{3.8019056342797985`*^9, 
  3.80190564123263*^9}},ExpressionUUID->"2d17ed46-3f53-4e8e-8734-\
96af61842cbe"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"\:5206\:5e03", "=", 
   RowBox[{"ProbabilityDistribution", "[", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"Which", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"0", "<", "y"}], " ", "&&", " ", 
        RowBox[{"0", "<", "x"}]}], ",", 
       RowBox[{"E", "^", 
        RowBox[{"(", 
         RowBox[{"-", 
          RowBox[{"(", 
           RowBox[{"x", "+", "y"}], ")"}]}], ")"}]}], ",", "True", ",", "0"}],
       "]"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "Infinity"}], ",", "Infinity"}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "Infinity"}], ",", "Infinity"}], "}"}]}], 
    "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"PDF", "[", 
   RowBox[{
    RowBox[{"MarginalDistribution", "[", 
     RowBox[{"\:5206\:5e03", ",", "1"}], "]"}], ",", "x"}], "]"}], 
  RowBox[{
  "(*", "x\:7684\:8fb9\:7f18\:6982\:7387\:5bc6\:5ea6", "*)"}]}]}], "Input",
 CellChangeTimes->{{3.8019059874772367`*^9, 3.8019060412168493`*^9}, {
  3.8019060760486374`*^9, 3.8019061264226665`*^9}, {3.8019061674377575`*^9, 
  3.801906263967907*^9}, {3.801917807092348*^9, 3.8019178080284605`*^9}, {
  3.80274272869736*^9, 3.8027427602780666`*^9}},
 CellLabel->"In[1]:=",ExpressionUUID->"8944f164-15bc-4d03-87f6-fed4fb6ef3d9"],

Cell[BoxData[
 TagBox[GridBox[{
    {"\[Piecewise]", GridBox[{
       {
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{"-", "x"}]], 
        RowBox[{"x", ">", "0"}]},
       {"0", 
        TagBox["True",
         "PiecewiseDefault",
         AutoDelete->True]}
      },
      AllowedDimensions->{2, Automatic},
      Editable->True,
      GridBoxAlignment->{
       "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
        "RowsIndexed" -> {}},
      GridBoxItemSize->{
       "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.84]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}},
      Selectable->True]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxItemSize->{
    "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[0.35]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  "Piecewise",
  DeleteWithContents->True,
  Editable->False,
  SelectWithContents->True,
  Selectable->False]], "Output",
 CellChangeTimes->{{3.801906078102858*^9, 3.801906096498931*^9}, 
   3.8019061266240215`*^9, {3.80190616869503*^9, 3.8019061906623087`*^9}, 
   3.802742778248026*^9},
 CellLabel->"Out[2]=",ExpressionUUID->"fa6020f5-2fb1-4dc1-bfe9-f4e512ed8f88"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"PDF", "[", 
   RowBox[{
    RowBox[{"MarginalDistribution", "[", 
     RowBox[{"\:5206\:5e03", ",", "2"}], "]"}], ",", "y"}], "]"}], 
  RowBox[{
  "(*", "y\:7684\:8fb9\:7f18\:6982\:7387\:5bc6\:5ea6", "*)"}]}]], "Input",
 CellChangeTimes->{{3.801906244623702*^9, 
  3.801906255507512*^9}},ExpressionUUID->"cc30807b-6636-406f-b701-\
068e8721b229"],

Cell[BoxData[
 TagBox[GridBox[{
    {"\[Piecewise]", GridBox[{
       {
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{"-", "y"}]], 
        RowBox[{"y", ">", "0"}]},
       {"0", 
        TagBox["True",
         "PiecewiseDefault",
         AutoDelete->True]}
      },
      AllowedDimensions->{2, Automatic},
      Editable->True,
      GridBoxAlignment->{
       "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
        "RowsIndexed" -> {}},
      GridBoxItemSize->{
       "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.84]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}},
      Selectable->True]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxItemSize->{
    "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[0.35]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  "Piecewise",
  DeleteWithContents->True,
  Editable->False,
  SelectWithContents->True,
  Selectable->False]], "Output",
 CellChangeTimes->{3.8019062469253674`*^9},
 CellLabel->"Out[15]=",ExpressionUUID->"f8ec1b03-d19e-4902-9114-dd643d40d163"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Probability", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"x", "+", "y"}], "<", "1"}], ",", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"x", ",", "y"}], "}"}], "\[Distributed]", "\:5206\:5e03"}]}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.801906268265216*^9, 3.80190628784382*^9}},
 CellLabel->"In[16]:=",ExpressionUUID->"8c29d7d5-7d14-4a19-bce8-f6b8e50317c7"],

Cell[BoxData[
 FractionBox[
  SuperscriptBox[
   RowBox[{"(", 
    RowBox[{
     RowBox[{"-", "1"}], "+", 
     SqrtBox["\[ExponentialE]"]}], ")"}], "2"], "\[ExponentialE]"]], "Output",
 CellChangeTimes->{3.8019062885213165`*^9},
 CellLabel->"Out[16]=",ExpressionUUID->"812e6e4d-82cb-4da4-94fb-3bdd1264b0ee"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"PDF", "[", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"TransformedDistribution", "[", 
    RowBox[{
     RowBox[{"x", "/", "y"}], ",", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y"}], "}"}], "\[Distributed]", "\:5206\:5e03"}]}], 
    "]"}], ",", "z"}], "\[IndentingNewLine]", "]"}]], "Input",
 CellChangeTimes->{{3.8019063094461226`*^9, 3.801906363332255*^9}, {
  3.8027427837520247`*^9, 3.802742784248025*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"8b8e38a9-1849-47c1-a3c1-5aa954739aee"],

Cell[BoxData[
 TagBox[GridBox[{
    {"\[Piecewise]", GridBox[{
       {
        FractionBox["1", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{"1", "+", "z"}], ")"}], "2"]], 
        RowBox[{"z", ">", "0"}]},
       {"0", 
        TagBox["True",
         "PiecewiseDefault",
         AutoDelete->True]}
      },
      AllowedDimensions->{2, Automatic},
      Editable->True,
      GridBoxAlignment->{
       "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
        "RowsIndexed" -> {}},
      GridBoxItemSize->{
       "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.84]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}},
      Selectable->True]}
   },
   GridBoxAlignment->{
    "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
     "RowsIndexed" -> {}},
   GridBoxItemSize->{
    "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
     "RowsIndexed" -> {}},
   GridBoxSpacings->{"Columns" -> {
       Offset[0.27999999999999997`], {
        Offset[0.35]}, 
       Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
       Offset[0.2], {
        Offset[0.4]}, 
       Offset[0.2]}, "RowsIndexed" -> {}}],
  "Piecewise",
  DeleteWithContents->True,
  Editable->False,
  SelectWithContents->True,
  Selectable->False]], "Output",
 CellChangeTimes->{{3.8019063584627075`*^9, 3.8019063641968393`*^9}, 
   3.8027427846890745`*^9},
 CellLabel->"Out[3]=",ExpressionUUID->"4cd28c3f-4f39-4e5b-86de-2e188e4b5813"]
}, Open  ]],

Cell["\:65b9\:6cd5\:ff1a\:5148\:8ba1\:7b97 CDF\:ff0c\:6761\:4ef6\:8f6c\:5316\
\:6210\:4e8c\:91cd\:79ef\:5206\:ff0c\:7136\:540e\:518d\:5173\:4e8e a \:6c42\
\:5bfc", "Subsubsection",
 CellChangeTimes->{{3.8027436096577096`*^9, 
  3.8027436528877125`*^9}},ExpressionUUID->"1d544619-a890-435b-8785-\
541731f752d4"]
}, Open  ]]
},
WindowSize->{958, 978},
WindowMargins->{{-8, Automatic}, {Automatic, 0}},
Magnification:>1.6 Inherited,
FrontEndVersion->"11.3 for Microsoft Windows (64-bit) (2018\:5e743\:670828\
\:65e5)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 182, 3, 106, "Section",ExpressionUUID->"2d17ed46-3f53-4e8e-8734-96af61842cbe"],
Cell[CellGroupData[{
Cell[787, 29, 1408, 35, 373, "Input",ExpressionUUID->"8944f164-15bc-4d03-87f6-fed4fb6ef3d9"],
Cell[2198, 66, 1806, 50, 75, "Output",ExpressionUUID->"fa6020f5-2fb1-4dc1-bfe9-f4e512ed8f88"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4041, 121, 380, 10, 110, "Input",ExpressionUUID->"cc30807b-6636-406f-b701-068e8721b229"],
Cell[4424, 133, 1684, 48, 75, "Output",ExpressionUUID->"f8ec1b03-d19e-4902-9114-dd643d40d163"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6145, 186, 382, 10, 76, "Input",ExpressionUUID->"8c29d7d5-7d14-4a19-bce8-f6b8e50317c7"],
Cell[6530, 198, 308, 8, 94, "Output",ExpressionUUID->"812e6e4d-82cb-4da4-94fb-3bdd1264b0ee"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6875, 211, 534, 12, 179, "Input",ExpressionUUID->"8b8e38a9-1849-47c1-a3c1-5aa954739aee"],
Cell[7412, 225, 1789, 51, 93, "Output",ExpressionUUID->"4cd28c3f-4f39-4e5b-86de-2e188e4b5813"]
}, Open  ]],
Cell[9216, 279, 310, 5, 110, "Subsubsection",ExpressionUUID->"1d544619-a890-435b-8785-541731f752d4"]
}, Open  ]]
}
]
*)