# 1. In each of the following models, find the Bayes risk and the Bayes estimator, using squared error

1. In each of the following models, find the Bayes risk and the Bayes estimator, using squared error loss. (a) X ~ Binomial(n, p), p ~ Beta(a, ß). 12.9 Exercises 205 (b) X ~ Poisson(?), ? ~ Gamma(a, ß). (c) X ~ N(?, s2) where s2 is known and ? ~ N(a, b2). 2. Let X1,…,Xn ~ N(?, s2) and suppose we estimate ? with loss function L(?, ? )=(? – ? )2/s2. Show that X is admissible and minimax. 3. Let T = {?1,…,?k} be a finite parameter space. Prove that the posterior mode is the Bayes estimator under zero–one loss

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