1. Let X1, ..., X n be a random sample from a Poisson distribution with mean A. Let the prior distribution of 11 be gamma with parameters a: and 6, where a and 9 are known. a) Find the posterior distribution of/l given X1 = x1, ..., Xn = xn. b) For the squared error loss function, find the Bayesian estimate of )L c) Find the maximum likelihood estimate of A. d) Rewrite the Bayesian estimate of A from part b) as a linear function of the MLE estimate from part c)