Question

考研数学概率论这个期望值怎么求？

我知道他的期望是5，但是怎么算出来呢？

Answer 1

这是典型的超几何分布

把红球当作次品

EX=10•10/20=5

Answer 2

X红球的数目

P(X=0) =C(10,10)/C(20,10) = 1/14756
P(X=1) =C(1,10).C(9,10)/C(20,10) = 100/184756
P(X=2) =C(2,10).C(8,10)/C(20,10) = 2025/184756
P(X=3) =C(3,10).C(7,10)/C(20,10) = 14400/184756
P(X=4) =C(4,10).C(6,10)/C(20,10) = 44100/184756
P(X=5) =C(5,10).C(5,10)/C(20,10) = 63504/184756
P(X=6)=P(X=4)=44100/184756
P(X=7)=P(X=3)=14400/184756
P(X=8)=P(X=2)=2025/184756
P(X=9)=P(X=1)=100/184756
P(X=10)=P(X=0)=1/184756
E(X)
=∑(i:0->10) i.P(X=i)
=(0)(1/14756) +(1)(100/184756)+(2)(2025/184756)+(3)(14400/184756)
+(4)(44100/184756) +(5)(63504/184756) +(6)(44100/184756) +(7)(14400/184756)
=(8)(2025/184756) +(9)(100/184756)+(10)(1/184756)
=923780/184756