Suppose that the random variables X1, . . . , Xk are independent and that Xi has the Poisson distribution with mean λi (i = 1, . . . , k). Show that for each fixed positive integer n, the conditional distribution of the random vector X = (X1, . . . , Xk), given that = n, is the multinomial distribution with parameters n and p = (p1, . . . , pk), where

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for i = 1. ..., k. Σ Pi=