Question

Let X and Y be independent rv's with pmf Pois(11) and Pois(12), respectively. (a) Find the distribution of Z= X+Y. (b) Find the distribution of X|X +Y. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p). Find the distribution of Y.

Let X and Y be independent rv’s with pmf Pois(λ1) and Pois(λ2), respectively.

(a) Find the distribution of Z = X + Y .
(b) Find the distribution of X|X + Y .

(c)If X∼Pois(λ1) and Y|X=x∼Bin(x,p). Find the distribution of Y.

Answer 1

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