# Question: Suppose that Xi i 1 2 3 are independent

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. Find its joint probability mass function. That is, find P{X = n, Y = m}.

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