设随机变量X和Y独立,且在(0,θ)上服从均匀分布,则E[min(X,Y)]等于(  )A.θ2B.θC.θ3D.

2025-05-20 04:24:55
推荐回答(1个)
回答1:

由题意得:
X,Y~U(0,θ)
则E(X)=E(Y)=

θ
2

z=MIN{X,Y}
Fmin(z)=1?[1?F(z)]2=1-(1?
1
θ
)2

fmin(z)=Fmin′(z)=
E(z)=
θ
3

故答案选:C