(10 points) Suppose that X,, : 1,2,3, are independent Poisson random variables with respective means A,,i : 1, 2, 3. Let X : X1 + X2 and Y : X1 + X3, then the pair (X, Y) is said to have a bivariate Poisson distribution. (a) Find the correlation p(X, Y) between X and Y. (b) Find the joint probability mass function P(X : i,Y : j), i,j : 0, 1