# 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}.

## Relevant Questions

Suppose X and Y are both integer-valued random variables. Let p(i|j) = P(X = i|Y = j) and q(j|i) = P(Y = j|X = i) Show that Let W be a gamma random variable with parameters (t, β), and suppose that conditional on W = w, X1, X2, . . . ,Xn are independent exponential random variables with rate w. Show that the conditional distribution of W given ...Suggest a procedure for using Buffon’s needle problem to estimate π. Surprisingly enough, this was once a common method of evaluating π. Let X1, . . . ,Xn be independent exponential random variables having a common parameter λ. Determine the distribution of min(X1, . . . ,Xn). In the text, we noted that when the Xi are all nonnegative random variables. Since an integral is a limit of sums, one might expect that whenever X(t), 0 ≤ t < ∞, are all nonnegative random variables; and this result is ...Post your question