Question

一个袋中装有8个大小质地相同的球,其中4个红球,4个白球,现从中任取四个球,设X为取得红球个数（1）求x分布列（2）若摸

Answer 1

(1)

x=0,1,2,3,4

P(x=0)=C(4,0)*C(4,4)/C(8,4)=1/70

P(x=1)=C(4,1)*C(4,3)/C(8,4)=16/70

P(x=2)=C(4,2)*C(4,2)/70=36/70

P(x=3)=C(4,3)*C(4,1)/C(8,4)=16/70

P(x=4)=C(4,4)*C(4,0)/C(8,4)=1/70

x 0 1 2 3 4

P 1/70 16/70 36/70 16/70 1/70

(2)

记得分为y,则

P(y=5)=P(x=4)=1/70

P(y=4)=P(x=3)=16/70

P(y=2)=P(x=2)+P(x=1)+P(x=0)=53/70

E(y)=5*1/70+4*16/70+2*53/70=35/14

有问题,