考研数学概率论浙大内部课件（盛骤）_概率论_其他

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/628009dcebb030486d2b4bc9/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/628009dcebb030486d2b4bc9/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">1</div></div><div class="c x0 y3 w3 h4"><div class="t m0 x2 h5 y4 ff2 fs1 fc1 sc0 ls0 ws0"> </div><div class="t m0 x3 h5 y5 ff2 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x4 h5 y4 ff2 fs1 fc1 sc0 ls0 ws0">概 率 论</div><div class="t m0 x5 h5 y5 ff2 fs1 fc0 sc0 ls0 ws0">概 率 论</div></div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/628009dcebb030486d2b4bc9/bg2.jpg"><div class="t m0 x6 h6 y6 ff3 fs2 fc1 sc0 ls0 ws0">2</div><div class="c x0 y3 w3 h4"><div class="t m0 x7 h7 y7 ff3 fs3 fc2 sc0 ls0 ws0">第三章 多维随机变<span class="_ _0"></span>量及其分布</div><div class="t m0 x8 h8 y8 ff3 fs4 fc1 sc0 ls0 ws0">关键词：</div><div class="t m0 x9 h8 y9 ff3 fs4 fc3 sc0 ls0 ws0">二维随机变量</div><div class="t m0 x9 h8 ya ff3 fs4 fc3 sc0 ls0 ws0">分布函数 分布律<span class="_ _1"></span> 概率密度</div><div class="t m0 x9 h8 yb ff3 fs4 fc3 sc0 ls0 ws0">边缘分布函数<span class="_ _1"></span> 边缘分布律 边缘概<span class="_ _1"></span>率密度</div><div class="t m0 x9 h8 yc ff3 fs4 fc3 sc0 ls0 ws0">条件分布函数<span class="_ _1"></span> 条件分布律 条件概<span class="_ _1"></span>率密度</div><div class="t m0 x9 h8 yd ff3 fs4 fc3 sc0 ls0 ws0">随机变量的独<span class="_ _1"></span>立性</div><div class="t m0 x9 h8 ye ff3 fs4 fc3 sc0 ls0 ws0">Z=X+Y<span class="_ _2"> </span>的概率密度</div><div class="t m0 x9 h8 yf ff3 fs4 fc3 sc0 ls0 ws0">M=max(X,Y)<span class="_ _2"> </span>的概率<span class="_ _1"></span>密度</div><div class="t m0 x9 h8 y10 ff3 fs4 fc3 sc0 ls0 ws0">N=min(X,Y)<span class="_ _2"> </span>的概率密度</div></div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/628009dcebb030486d2b4bc9/bg3.jpg"><div class="c x0 y3 w3 h4"><div class="t m0 x6 h6 y11 ff3 fs2 fc1 sc0 ls0 ws0">3</div><div class="t m0 xa h9 y12 ff3 fs5 fc1 sc0 ls0 ws0">§1 <span class="_ _3"> </span>二维随机变量</div><div class="t m0 xb ha y13 ff3 fs6 fc1 sc0 ls0 ws0">问题的提<span class="_ _1"></span>出</div><div class="t m0 xc hb y14 ff3 fs7 fc1 sc0 ls0 ws0">例<span class="_ _2"> </span>1<span class="_ _4"> </span>：研究某一地区学龄儿童的发育情况。仅研究身</div><div class="t m0 xc hb y15 ff3 fs7 fc1 sc0 ls0 ws0">高<span class="_ _4"> </span><span class="sc1">H<span class="_ _2"> </span></span>的分布或仅研究体重<span class="_ _4"> </span><span class="sc1">W<span class="_ _2"> </span></span>的分布是不够的。需</div><div class="t m0 xc hb y16 ff3 fs7 fc1 sc0 ls0 ws0">要同时考察每个儿童的身高和体重值，研究身<span class="_ _5"> </span>高和体</div><div class="t m0 xc hb y17 ff3 fs7 fc1 sc0 ls0 ws0">重之间的关系，这就要引入定义在同一<span class="_ _5"> </span>样本空间的两</div><div class="t m0 xc hb y18 ff3 fs7 fc1 sc0 ls0 ws0">个随机变量。</div><div class="t m0 xc hb y19 ff3 fs7 fc1 sc0 ls0 ws0">例<span class="_ _4"> </span>2<span class="_ _2"> </span>：研究某种型号炮弹的弹着点分布。每枚炮弹的</div><div class="t m0 xc hb y1a ff3 fs7 fc1 sc0 ls0 ws0">弹着点位置需要由横坐标和纵坐标来确定，而<span class="_ _5"> </span>它们是</div><div class="t m0 xc hb y1b ff3 fs7 fc1 sc0 ls0 ws0">定义在同一样本空间的两个随机变量。</div></div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div>

<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/628009dcebb030486d2b4bc9/bg4.jpg"><div class="c x0 y3 w3 h4"><div class="t m0 x6 h6 y11 ff3 fs2 fc1 sc0 ls0 ws0">4</div><div class="t m0 xd hc y1c ff3 fs8 fc1 sc0 ls0 ws0">定义：设<span class="_ _6"> </span>E<span class="_ _6"> </span>是一个随机试验，样本空间<span class="_ _6"> </span>S={e}<span class="_ _7"> </span>；</div><div class="t m0 xe hc y1d ff3 fs8 fc1 sc0 ls0 ws0">设<span class="_ _6"> </span>X=X(e)<span class="_ _7"> </span>和<span class="_ _6"> </span>Y=Y(e)<span class="_ _7"> </span>是定义</div><div class="t m0 xe hc y1e ff3 fs8 fc1 sc0 ls0 ws0">在<span class="_ _6"> </span>S<span class="_ _6"> </span>上<span class="_ _0"></span>的随机变量，由它们构成的</div><div class="t m0 xe hc y1f ff3 fs8 fc1 sc0 ls0 ws0">向量<span class="_ _6"> </span>(X,Y)<span class="_ _7"> </span>叫做<span class="sc1">二维随机向量</span></div><div class="t m0 xe hc y20 ff3 fs8 fc1 sc0 ls0 ws0">或<span class="sc1">二维随机变量</span>。</div><div class="t m1 xf hd y21 ff4 fs9 fc1 sc0 ls0 ws0"><span class="_ _8"> </span></div><div class="t m2 x10 he y22 ff1 fsa fc1 sc0 ls0 ws0">(<span class="_ _9"> </span>,<span class="_ _a"> </span>)<span class="_ _b"> </span>(<span class="_ _c"> </span>)<span class="_ _d"> </span>(<span class="_ _e"> </span>)</div><div class="t m2 x11 he y23 ff1 fsa fc1 sc0 ls0 ws0"> <span class="_ _f"> </span>(<span class="_ _c"> </span>,<span class="_ _10"> </span>)</div><div class="t m2 x11 hf y22 ff5 fsa fc1 sc0 ls0 ws0">F<span class="_ _11"> </span>x<span class="_ _12"> </span>y<span class="_ _13"> </span>P<span class="_ _d"> </span>X<span class="_ _14"> </span>x<span class="_ _15"> </span>Y<span class="_ _14"> </span>y</div><div class="t m2 x12 hf y23 ff5 fsa fc1 sc0 ls0 ws0">P<span class="_ _12"> </span>X<span class="_ _16"> </span>x<span class="_ _17"> </span>Y<span class="_ _14"> </span>y</div><div class="t m2 x13 h10 y22 ff4 fsa fc1 sc0 ls0 ws0"><span class="_ _18"> </span><span class="_ _19"> </span></div><div class="t m2 x14 h10 y23 ff4 fsa fc1 sc0 ls0 ws0"><span class="_ _1a"></span><span class="_ _1b"> </span><span class="_ _1c"> </span></div><div class="t m2 x15 h10 y22 ff4 fsa fc1 sc0 ls0 ws0"></div><div class="t m3 x16 h11 y24 ff3 fsb fc1 sc0 ls0 ws0">记成</div><div class="t m0 x17 h12 y25 ff6 fsc fc2 sc0 ls0 ws0">0</div><div class="t m4 x18 h13 y26 ff5 fsd fc1 sc0 ls0 ws0">x</div><div class="t m5 x19 h14 y27 ff4 fse fc1 sc0 ls0 ws0"><span class="_ _1d"> </span></div><div class="t m0 x1a h15 y28 ff1 fsf fc1 sc0 ls0 ws0">,<span class="_ _1e"></span><span class="ff5">x<span class="_ _1f"> </span>y</span></div><div class="t m6 x1b h16 y29 ff5 fs10 fc1 sc0 ls0 ws0">y</div><div class="t m0 x1c h17 y2a ff7 fs8 fc2 sc0 ls0 ws0">S</div><div class="t m0 x1d h17 y2b ff7 fs8 fc2 sc0 ls0 ws0">e</div><div class="t m7 x1e h18 y2c ff5 fs11 fc1 sc0 ls0 ws0">y</div><div class="t m8 x1f h19 y2d ff4 fs12 fc1 sc0 ls0 ws0"><span class="_ _1f"> </span><span class="_ _d"> </span><span class="_ _1f"> </span></div><div class="t m9 x20 h1a y2e ff4 fs13 fc1 sc0 ls0 ws0"><span class="_ _20"> </span></div><div class="t m0 x21 h1b y2f ff1 fs14 fc1 sc0 ls0 ws0">,<span class="_ _21"></span><span class="ff5">X<span class="_ _12"> </span>e<span class="_ _22"> </span>Y<span class="_ _1f"> </span>e</span></div><div class="t m4 x22 h13 y30 ff5 fsd fc1 sc0 ls0 ws0">x</div><div class="t m0 x23 hc y31 ff3 fs8 fc1 sc0 ls0 ws0">定义：设<span class="_ _6"> </span>(X,Y)<span class="_ _7"> </span>是二维随机变量对于任意实数<span class="_ _2"> </span>x<span class="_ _0"></span>,y<span class="_ _6"> </span>，</div><div class="t m0 x24 hc y32 ff3 fs8 fc1 sc0 ls0 ws0">二元函数</div><div class="t m0 x23 hc y33 ff3 fs8 fc1 sc0 ls0 ws0">称为<span class="sc1">二维随机变量<span class="_ _6"> </span>(X,Y)<span class="_ _6"> </span>的分布函数。</span></div></div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div>