Suppose that Xi, i = 1,2,3, are independent Poisson random variables with respective means...

Suppose that Xi, i = 1,2,3, are independent Poisson random variables with respective means λi, i = 1,2,3. Let X = X1 + X2 and Y = X2 + X3. The random vector X, Y is said to have a bivariate Poisson distribution.

(a) Find E[X] and E[Y].

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(b) Find Cov(X, Y).

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(c) Find the joint probability mass function P{X = i, Y = j}