Paper 2, Section I, F

Probability | Part IA, 2018

Let XX and YY be independent Poisson random variables with parameters λ\lambda and μ\mu respectively.

(i) Show that X+YX+Y is Poisson with parameter λ+μ\lambda+\mu.

(ii) Show that the conditional distribution of XX given X+Y=nX+Y=n is binomial, and find its parameters.

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