Question

设随机变量X与Y相互独立,且服从同一分布,X的分布律为

Answer 1

由于:P(X=0,Y=0)=P(X=1,Y=0)=P(X=0,Y=1)=P(X=1,Y=1)= 1/4.

P(Z=1)= P(X=1,Y=0)+ P(X=0,Y=1)+ P(X=1,Y=1)= 3/4.

P(Z=0) =:P(X=0,Y=0) =1/4..

Z的分布律:P(Z=0)=1/4,P(Z=1) = 3/4.