1. Suppose that Y is a binomial RV based on n trials and success probability p. a. Use the conjugate beta prior with parameters a and B to derive the posterior distribution of ply b. Now consider the conjugate prior with parameters a = 1 and B = 1. Now derive the Bayes estimator for p. C. Find the MSE of the Bayes estimator found in part (b). I d. For what values of p is the MSE of the Bayes estimator smaller than that of the maximum likelihood estimator of p. Illustrate with n = 1 to find the range of values of p. 1. Suppose that Y is a binomial RV based on n trials and success probability p. a. Use the conjugate beta prior with parameters a and B to derive the posterior distribution of ply b. Now consider the conjugate prior with parameters a = 1 and B = 1. Now derive the Bayes estimator for p. C. Find the MSE of the Bayes estimator found in part (b). I d. For what values of p is the MSE of the Bayes estimator smaller than that of the maximum likelihood estimator of p. Illustrate with n = 1 to find the range of values of p