Suppose X1, ..., Xn Exponential(71), where A is unknown. (a) Find the maximum likelihood estimator (MLE) ) for A. Show that 1 is a maximum. (b) Give two sufficient statistics for 1, and state the theorem(s) you used to deter- mine that they are sufficient. (c) Show that Y = 1 is a biased estimator for 1. Hint: If V1, ..., Vn Exponential(0), then U = Et, Vi ~Gamma(n, 0) and fu(u) = Injun-le- Ou. (d) Suppose we give A a prior distribution 7 ()) that is Gamma(a, B), i.e. 7(A) =\\"-de PA where a > 0 and B > 0 are known. Find the posterior distribution ()|x) for 1. (e) Find the Bayes estimator of A using squared loss