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3. Suppose that the random variable Y has a binomial distribution with n trials and success probability p, where n is a given constant

3. Suppose that the random variable Y has a binomial distribution with n trials and success probability p, where n is a given constant and p is a uniform (0,1) random variable. (a) Find E(Y) and Var(Y). [10 marks] (b) Find the marginal probability mass function of Y. [10 marks] (c) Find E(p|Y=y). [10 marks] [Total: 30 marks]

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