Let X and Y be independent random variables where px (k) e k k and pY(k) e k k for k 0, 1, Show that the conditional pdf of X given that X Y n is binomial with parameters n and

Question: Let X and Y be independent random variables where px (k) = e k/k! and pY(k) = e k/k! for k = 0, 1, .

Let X and Y be independent random variables where px (k) = e−λ λk/k! and pY(k) = e−μ μk/k! for k = 0, 1, . . . . Show that the conditional pdf of X given that X + Y = n is binomial with parameters n and λ/λ + μ.

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