1. The problem statement, all variables and given/known data Let X ~ Exponential(3) and Y ~ Poisson(5). Assume X and Y are independent. Let Z = X + Y. Compute the Cov(X,Z). 2. Relevant equations I know Cov(X, Z) = E(XZ) - E(X)E(Z). But how do I compute E(XZ) and E(Z) ?? Since for E(XZ), I would need the pdf/pmf (Exp is abs cts, while Poisson is discrete). Or can I do the following: 3. The attempt at a solution Cov (X, Z) = Cov(X, X + Y) = Cov(X, X) + Cov(X,Y) = Var(X) + Cov(X,Y) Since X, Y indep., Cov(X,Y) = 0 = Var(X) Is this the correct derivation? Any help would be greatly appreciated, as the exam is just around the corner. Thanks.