1. The problem statement, all variables and given/known data Suppose X1,X2,... are independent each having exponential distirbution with parameter lambda and N has a Poisson(lambda) distribution and is independent of the Xi's. You are given that the moment generating function of a Gamma(alpha,lambda) variable is m(t)=[lambda/(lambda-t)]alpha Find the moment generating function of SN=X1+X2+...+XN 2. Relevant equations Just in case you are confused about the parameters above. Poisson(lambda) =>E(W)=Var(W)=lambda W~Gamma(alpha,lambda) => E(W)=alpha/lambda, Var(W)=alpha/lambda^2 3. The attempt at a solution I know that the moment generating function of a sum of indepedent random variables is the product of the moment generating functions of each random variable. But here we have capital "N" and N follows some other distribution as well. This really scares me off...and I have no clue what to do in this case... Does anyone have any idea? Please help!