Question

设随机变量X的概率分布为p(X=k)=a^k/((a+1)^(k+1)),(k=0,1,2...)

Answer 1

E（x） = a/((a+1)^2)*∑k*(a/(a+1))*^(k-1) = a/((a+1)^2)*(∑(a/(a+1))*^k)'

因为∑(a/(a+1))*^k = ∑x^k=x/(1-x) (其中x=a/(a+1))

E(x) = a/((a+1)^2)*(∑(a/(a+1))*^k)' = a