Let X be the number of customers arriving in a given minute at the drive-up window of a local bank, and let Y be the number who make withdrawals. Assume that X is Poisson distributed with expected value E(X) = 3, and that the conditional expectations and variance of Y given X = x are E(Y | x) = x/2 and Var(Y | x) = (x + 1)/3.

(a) Find E(Y).

(b) Find Var(Y).

(c) Find E(XY).