1. The problem statement, all variables and given/known data Let X1...XN be independent and identically distributed random variables, N is a non-negative integer valued random variable. Let Z = X1 + ... + XN (assume when N=0 Z=0). 1. Find E(Z) 2. Show var(Z) = var(N)E(X1)2 + E(N)var(X1) 2. Relevant equations E(Z) = EX (E(X|Z)) Law of total variance: var(Z) = EX (var(Z|X)) + VarX (E(Z|X)) 3. The attempt at a solution 1. I think I have managed this, I got E(N)E(X) 2. I'm unsure how to tackle this one, I know var(Z) = E(Z2) - E(Z)2, and I know E(Z)2 but I don't know how to calculate the other, or if I should be using the equation above, and if so, how.