Suppose that X1,X2,........Xn is a random sample from an exponential distribution with pdf : f(x|)=e-X I(x>0). is unknown. Suppose that the prior distribution of is a gamma distribution with given parameters and (>0, >0). 1) Show that the posterior distribution of given the observations is again a gamma distribution. Find the parameters of the posterior gamma distribution 2) Find the Bayes estimator of with squared error loss function 3) Find the Bayes risk (I(x>0) is the indicator function)