Question: 9. Let X have a Poisson distribution with parameter A, and given that X = n, let Y have a binomial distribution with parameters n

9. Let X have a Poisson distribution with parameter A, and given that X = n, let Y have a binomial distribution with parameters n and p. (a) What is the joint probability mass function of X and Y? 5 mins (b) Show that the marginal distribution of Y is a Poisson distribution with parameter Ap. [10 mins (c) What is the conditional distribution of X conditional on Y = ? 10 mins

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