Question: Suppose that X1 and X2 are independent random variables, that X1 has the binomial distribution with parameters n1 and p, and that X2 has the

Suppose that X1 and X2 are independent random variables, that X1 has the binomial distribution with parameters n1 and p, and that X2 has the binomial distribution with parameters n2 and p, where p is the same for both X1 and X2. For each fixed value of k (k = 1, 2, . . . , n1 + n2), prove that the conditional distribution of X1 given that X1 + X2 = k is hypergeometric with parameters n1, n2, and k.

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