Problem 1 Suppose that X1, ..... X,0 are lid Poisson( A) random variables. (a) For the observed sample 5, 8, ,6, 6, 3, 1, ,4, 2, 5, 4 find AMy using two different moments. Here MM refers to Method of Mo- ments estimator. (b) Find the Bayes estimator for squared error loss for A when using prior E(1) r(4,1). (c) Find AMLE and state its distribution. (d) Derive an expression for P(| A - A [> 1 | A = 4) for AMLE and ARages and state the distribution of the sample statistic the estimator is based on in each Case