# Question

Let X1, X2, . . . , Xn be a random sample from a Poisson distribution with mean λ > 0. Find the conditional probability P(X1 = x1, . . . , Xn = xn | Y = y), where Y = X1 + · · · + Xn and the nonnegative integers x1, x2, . . . , xn sum to y. Note that this probability does not depend on λ.

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