设随机变量X的分布律为P(X=k)=1/2^k,k=1,2,….求：P=(X=3的倍数).

Question

如题所述

Answer 1

P(X=3的倍数)=P(X=3)+P(X=6)+P(X=9)+…+P(X=3n)+…
=(1/2)^3+(1/2)^6+(1/2)^9+…+(1/2)^3n+…
=(1/8)/(1-1/8)
=1/7