Please provide the complete solution process of this question, thank you!

(for graduate credit) Let X be a discrete random variable such that P(X = 11:) > 0 if and only if a: is a positive integer (i.e., a: = 0, l, 2, . . ) and E(X) 3:). HINT: You will need to work with partial sums in order to be careful about convergence of series. Start by showing lim nP(X > n) = 0. 71)00 Then consider the partial sum 22:1 ayP(X 2 at). Show that P(X = 51:) may be replaced by P(X > :c 1) P(X > cc). Rearrange the summation and let n > oo