Question

设随机变量X和Y相互独立且具有相同的分布,X的概率分布为 X -1 1 Pi 1/2 1/2 求P｛X=Y｝及P｛X>Y

Answer 1

P(X=Y) = P(X=-1,Y=-1) + P(X=1,Y=1)

= P(X=-1)P(Y=-1) + P(X=1)P(Y=1)

= 1/4 + 1/4 =1/2

P(X>Y) = P(X=1,Y=-1) = P(X=1)P(Y=-1) = 1/4