Question

x,y为独立分布的离散型随机变量 p(X=i）=p(Y=i)=1/2的i方 i=0,1..求z=x+y的概率分布

Answer 1

P(z=k)=∑p(x=i)P(y=k-i)=∑(1/2^i)(1/2^(k-i))=∑1/2^k

一共k+1个1/2^k

P(z=k)=(k+1)/2^k