1. Let X be a Poisson random variable with unknown mean 1. We model ) with a random variable A which is has a chi-squared distribution with 4 degrees of freedom. We take a random sample of X of size n, X1, ..., Xn. (a) Find the posterior distribution of A given that X1 = X1, . .., An = In. Hint. The posterior distribution will be one that you recognize, so it will be best to show that the posterior distribution is proportional to this familiar distribution.(b) 4' ' Compute the Bayesian estimator for A that minimizes the mean square error. Hint. If you recognize the distribution of the posterior, then you could just apply a estab- lished formula instead of having to compute an intergral. (c) Suppose that before the sampling takes place, a fellow researcher tells you that we are certain that, in fact, 0