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1、习题与解答3.1,1.一批产品中有一等品 50%，二等品 30%，三等品20%。从中有放回的抽出5件，以分别表示取出的5见中一等品、二等品的件数，求(X,Y)的联合分布列.解：这是一个三项分布，若驱除的5件中有i件一等品、j件二等品，则有5-i-j件三等品，所以当i=0,1, ,5, j=0,1, ,5, i+j5时，有 用表格形式表示如下：,1.00000,0.00243,0.02835,0.1323,0.3087,0.36015,0.16807,列和,0.03125,0.00000,0.00000,0.0000,0.0000,0.00000,0.03125,5,0.15625,0.0000
2、0,0.00000,0.0000,0.0000,0.09375,0.06250,4,0.31250,0.00000,0.00000,0.0000,0.1125,0.15000,0.05000,3,0.31250,0.00000,0.00000,0.0675,0.1350,0.09000,0.02000,2,0.15625,0.00000,0.02025,0.0540,0.0540,0.02400,0.00400,1,0.03125,0.00243,0.00810,0.0108,0.0072,0.00240,0.00032,0,行和,5,4,3,2,1,0,X Y,行和就是X的分布b(5,0.5
3、). 列和就是Y的分布b(5,0.3). P(X2,Y1)=0.09+0.135+0.0675+0.15+0.1125+0.09375=0.648752.100件产品中有50件一等品、30件二等品、20件三等品。从中部放回地抽取5件，以X、Y分别表示取出地5件中一等品、二等品地件数，求(X,Y)的联合分布。解：这是一个三维超几何分布，若取出的5件中有i件一等品、j件二等品，则有5-i-j件三等品，所以当i=0,1, ,5，j=0,1, ,5, i+j 5时，有用表格形式表示如下：,0.31891,0.00000,0.00000,0.06606,0.14156,0.09274,0.01855,2
4、,0.15295,0.00000,0.01820,0.05393,0.05489,0.02271,0.00322,1,0.02814,0.00189,0.00728,0.01024,0.00659,0.00193,0.00021,0,行和,5,4,3,2,1,0,X Y,3,0.31891,0.00000,0.00000,0.00000,0.11325,0.15620,0.04946,0.15295,0.00000,0.00000,0.00000,0.00000,0.09177,0.06118,4,5,0.02814,0.00000,0.00000,0.00000,0.00000,0.00000,0.02814,列和,1.00000,0.00189,0.02548,0.13023,0.31629,0.36535,0.16076,行和就是X的分布h(5,100,50)(超几何分布) 列和就是Y的分布h(5,100,30)(超几何分布) P(X2,Y1)=0.661583.盒子里有3个黑球、2个红球、2个白球，从中任取4个，以X表示取到黑球的个数，以Y表示取到红球的个数，试求P(X=Y).解 4.设随机变量 ，i=1,2的分布列如下，且满足P( =0)=1;试求P( ). 解 记（ , ）的联合分布列为,(3),
