Question

Problem 1: 15 points (= 5 + 5 + 5) You are given that an integer-valued random variable N has distribution such that P[N 2 n] = ()' for n 20. Non-negative random variables X = {Xx : k = 1, 2, ...,} do not depend on N and share the common distribution with density f*(x) = (216). 23.-6 valid for x > 0 Consider a random sum, 2N+5 S= XR. k1 1. Derive expectation of S, that is: ES] 2. Evaluate variance of S, that is: Var (S) 3. Find the marginal second moment of S, that is: E(S)