Suppose that Xi,i = 1,2,3 are independent Pois-son random variables with respective means X, 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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