(* 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[     10180,        297]
NotebookOptionsPosition[      8985,        265]
NotebookOutlinePosition[      9372,        282]
CellTagsIndexPosition[      9329,        279]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["\:77e9\:4f30\:8ba1", "Section",
 CellChangeTimes->{{3.801915745540351*^9, 3.801915748575431*^9}, {
  3.8019169646107635`*^9, 
  3.8019169679115973`*^9}},ExpressionUUID->"487d58d0-d891-4d69-9f8b-\
71eba966b654"],

Cell[CellGroupData[{

Cell[TextData[{
 "1. \:603b\:4f53\:7684\:5206\:5e03\:5e26\:672a\:77e5\:53c2\:6570\:ff0c\:8ba1\
\:7b97\:5b83\:7684\:6bd4\:5982EX\:ff0cDX\:ff0c\:4e5f\:5e26\:6709\:53c2\:6570\n\
2. \:53d6\:6837\:ff0c\:8ba1\:7b97\:6837\:672c\:7684 EX\:ff0cDX\:ff0c\:8fd9\
\:4e2a\:662f\:786e\:5b9a\:503c",
 StyleBox["\n",
  FontWeight->"Bold"],
 "3. \:89e3\:65b9\:7a0b\:7ec4\:ff0c\:5f97\:5230\:53c2\:6570\:7684\:503c"
}], "Subsection",
 CellChangeTimes->{{3.801918609628317*^9, 3.801918633942442*^9}, {
  3.801918669437626*^9, 
  3.801918683644884*^9}},ExpressionUUID->"74586e33-50d1-494c-8339-\
095ad7670bea"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"p", "[", 
    RowBox[{"x_", ",", "\[Theta]_"}], "]"}], "=", 
   TagBox[GridBox[{
      {"\[Piecewise]", GridBox[{
         {
          FractionBox[
           RowBox[{"2", 
            RowBox[{"\[Theta]", "^", "2"}]}], 
           RowBox[{
            RowBox[{"(", 
             RowBox[{
              RowBox[{"\[Theta]", "^", "2"}], "-", "1"}], ")"}], 
            RowBox[{"x", "^", "3"}]}]], 
          RowBox[{"1", "<", "x", "<", "\[Theta]"}]},
         {"0", "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]}], "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{"EX", "=", "X"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{"Integrate", "[", 
  RowBox[{
   RowBox[{"x", "*", 
    RowBox[{"p", "[", 
     RowBox[{"x", ",", "\[Theta]"}], "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "Infinity"}], ",", "Infinity"}], "}"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.801917099295065*^9, 3.8019172704799976`*^9}, {
  3.801917816835329*^9, 3.8019178431509976`*^9}, {3.8019179988438673`*^9, 
  3.801918015732086*^9}, {3.801918087220663*^9, 3.8019181509805727`*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"b0da6145-4170-43b5-81e5-35f4e9450f1a"],

Cell[BoxData[
 TagBox[GridBox[{
    {"\[Piecewise]", GridBox[{
       {
        FractionBox[
         RowBox[{"2", " ", 
          SuperscriptBox["\[Theta]", "2"]}], 
         RowBox[{
          SuperscriptBox["x", "3"], " ", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "1"}], "+", 
            SuperscriptBox["\[Theta]", "2"]}], ")"}]}]], 
        RowBox[{"1", "<", "x", "<", "\[Theta]"}]},
       {"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->{3.801918151340582*^9},
 CellLabel->"Out[8]=",ExpressionUUID->"43546b3d-8bb1-447e-970b-dc07585708c5"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    TagBox[GridBox[{
       {"\[Piecewise]", GridBox[{
          {
           FractionBox[
            RowBox[{"2", " ", "\[Theta]"}], 
            RowBox[{"1", "+", "\[Theta]"}]], 
           RowBox[{"\[Theta]", ">", "1"}]},
          {"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], "[", 
    RowBox[{"[", 
     RowBox[{"1", ",", "1", ",", "1"}], "]"}], "]"}], "\[Equal]", "X"}], "//", 
  RowBox[{
   RowBox[{"Solve", "[", 
    RowBox[{"#", ",", "X"}], "]"}], "&"}]}]], "Input",
 CellChangeTimes->{{3.801918163823761*^9, 3.801918199312518*^9}},
 CellLabel->"In[12]:=",ExpressionUUID->"e3adcfc0-09c7-419d-8ffc-4b8166f059fc"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"X", "\[Rule]", 
    FractionBox[
     RowBox[{"2", " ", "\[Theta]"}], 
     RowBox[{"1", "+", "\[Theta]"}]]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{{3.8019181678181543`*^9, 3.801918199524585*^9}},
 CellLabel->"Out[12]=",ExpressionUUID->"2415a208-21fa-40ff-acd4-099920592092"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["1. \:6781\:5927\:4f3c\:7136\:4f30\:8ba1", "Subsection",
 CellChangeTimes->{{3.801919460933153*^9, 3.8019194611361637`*^9}, {
  3.801919831117407*^9, 
  3.8019198372877812`*^9}},ExpressionUUID->"87548e6d-de34-42fc-a703-\
ea71eaa705f8"],

Cell["\<\
1. \:603b\:4f53\:7684\:5206\:5e03\:5e26\:672a\:77e5\:53c2\:6570\:ff0c\:8ba1\
\:7b97\:62bd\:6837\:7ed3\:679c\:7684 P
2. \:4ee4 P \:6700\:5927\
\>", "Subsubsection",
 CellChangeTimes->{{3.8019198661296377`*^9, 
  3.8019198868439503`*^9}},ExpressionUUID->"2228bdf6-966a-40f5-bac1-\
8f155015ef16"]
}, Open  ]]
}, Open  ]]
},
WindowSize->{981, 792},
WindowMargins->{{Automatic, 72}, {-12, Automatic}},
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, 216, 4, 106, "Section",ExpressionUUID->"487d58d0-d891-4d69-9f8b-71eba966b654"],
Cell[CellGroupData[{
Cell[821, 30, 588, 12, 210, "Subsection",ExpressionUUID->"74586e33-50d1-494c-8339-095ad7670bea"],
Cell[CellGroupData[{
Cell[1434, 46, 2523, 67, 179, "Input",ExpressionUUID->"b0da6145-4170-43b5-81e5-35f4e9450f1a"],
Cell[3960, 115, 1919, 55, 101, "Output",ExpressionUUID->"43546b3d-8bb1-447e-970b-dc07585708c5"]
}, Open  ]],
Cell[CellGroupData[{
Cell[5916, 175, 2104, 57, 111, InheritFromParent,ExpressionUUID->"e3adcfc0-09c7-419d-8ffc-4b8166f059fc"],
Cell[8023, 234, 339, 8, 78, "Output",ExpressionUUID->"2415a208-21fa-40ff-acd4-099920592092"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[8411, 248, 240, 4, 85, "Subsection",ExpressionUUID->"87548e6d-de34-42fc-a703-ea71eaa705f8"],
Cell[8654, 254, 303, 7, 110, "Subsubsection",ExpressionUUID->"2228bdf6-966a-40f5-bac1-8f155015ef16"]
}, Open  ]]
}, Open  ]]
}
]
*)