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Question: let x1x2 xk be independent poisson random...

Question details

Let X1,X2, · · · ,Xk be independent Poisson random variables with means μ1, μ2, · · · , μk
and let S = X1 + X2 + · · · + Xk. Given S = s,

what are the conditional distributions
of
(a) X1,
(b) X1 + X2, and
(c) (X1, X2)?

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