5. Let X, Y ~ Poisson(X) be independent Poisson rv's with the same parameter >> 0. (a) Find the joint pmf of X+Y and Y. (b) Find the marginal pmf of X + Y. (c) Find the conditional pmf of Y | (X+Y). File Pret

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solve a and b please

5. Let X, Y Poisson(X) be independent Poisson rv's with the same parameter λ > 0.
(a) Find the joint pmf of X + Y and Y.
(b) Find the marginal pmf of X+Y.
(c) Find the conditional pmf of Y | (X + Y).
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Transcribed Image Text:5. Let X, Y Poisson(X) be independent Poisson rv's with the same parameter λ > 0. (a) Find the joint pmf of X + Y and Y. (b) Find the marginal pmf of X+Y. (c) Find the conditional pmf of Y | (X + Y). File Preview
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