Question

设随机变量X与Y独立同分布,且X的分布率为p{x=-1}=2/3,p{x=1}=1/3,则Z=XY的分布率为?

Answer 1

p{Z=1} = P{ XY=1 } = P{ X=1,Y=1 }+P{ X=-1,Y=-1} = 2/3 * 2/3 + 1/3 * 1/3 = 5/9

p{Z=1} = P{ XY=-1 } = P{ X=-1,Y=1 }+P{ X=1,Y=-1} = 1/3 * 2/3 + 1/3 * 2/3 = 4/9

分布率：

p{Z=1}=5/9

p{Z=-1}=4/9