Suppose Xp ~ Binom(n, p), where n is known and P is unknown. (a) Compute the mean squared error (MSE) of the maximum likelihood estimator PMLE X n' (b) Assume the prior distribution p ~ Beta (a, ẞ). Compute the mean squared error (MSE) of the Bayes estimator with respect to the squared loss. (You don't need to derive the posterior distribution again if it was derived in class. Leave the final expression there if you cannot further simplify it.) (c) Assume the true success rate p = 1/2 and Jefferys prior p ~ Beta (½½, ½), which estimator is better in terms of MSE (for any fixed n)? Give your reasoning in terms of the variance and bias tradeoff. (d) Assume n = 10 and the true success rate p = 0.8. Is the maximum like- lihood estimator or the Bayes estimator (based on the Jefferys prior) better in terms of MSE? Give your reasoning in terms of the variance and bias tradeoff.