Refer to Exercise 16.6. If Y is a binomial random variable based on n trials and success

Chapter 16, Problem 16.8

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Refer to Exercise 16.6. If Y is a binomial random variable based on n trials and success probability p and p has the conjugate beta prior with parameters = 1 and = 1, a determine the Bayes estimator for p, p B. b what is another name for the beta distribution with = 1 and = 1? c find the mean square for error (MSE) of the Bayes estimator found in part (a). [Hint: Recall Exercise 8.17]. d For what values of p is the MSE of the Bayes estimator smaller than that of the unbiased estimator p = Y/n?

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