概率论与数理统计习题答案[1](3)

P(Y?0)?a?ab(a?b)22P(Y?1)?b?ab(a?b)22

P(X?0,Y?0)?P(X?0)P(Y?0)P(X?0,Y?1)?P(X?0)P(Y?1)P(X?1,Y?0)?P(X?1)P(Y?0)P(X?1,Y?1)?P(X?1)P(Y?1)

所以，X与Y相互独立。 （2）不放回抽样 P(X?0,Y?0)?a(a?1)(a?b)(a?b?1)P(X?0,Y?1)?ab(a?b)(a?b?1)

P(X?1,Y?0)?ab(a?b)(a?b?1)P(X?1,Y?1)?b(b?1)(a?b)(a?b?1)

P(X?0)?a(a?1)?ab(a?b)(a?b?1)P(X?1)?b(b?1)?ab(a?b)(a?b?1)

P(Y?0)?a(a?1)?ab(a?b)(a?b?1)P(Y?1)?b(b?1)?ab(a?b)(a?b?1)

?a(a?1)a2因为P(X?0,Y?0)(a?b)(a?b?1)?(a?b)2?P(X?0)P(Y?0)所以，X与Y不相互独立。 5． 解：当-1

fX(x)??1212x24xydy?218x2(1?x4)

所以有

ff(x,y)?2y?1?x?1,x2?y?1;YX(y|x)????1?x4,f

X(x)??0,其他。1P(Y?3y74|X?12)??2341?1dy?15

166．

11

(1)P(X?1,Y?0)?P(X?1,Y?0)?P(X?2,Y?0)?P(X?1,Y??1)?P(X?2,Y??1)?191(2)P(X?2|Y?0)?P(X?2,Y?0)?123P(Y?0)7?7 36

（3）因为P(X??1,Y??1)?0?P(X??1)P(Y??1) 所以，X，Y不相互独立

??7．解：fZ(z)??fX(x)fY(z?x)dx

??当0?z?1时，