= 8. Let X (X1,..., Xn) denote an iid sample of size n from Exp(0), where > 0 is the unknown scale parameter. (a) Find the Fisher information Ix-(0). (b) Find the Cramer-Rao lower bound for estimating 9. Then show that = X is an unbiased estimator whose variance equals the lower bound. (c) Consider estimating =02. Show that on = (1+)-1X2 is unbiased. (d) Find the Cramer Rao lower bound for estimating , and show that the variance of on defined above is strictly larger than the lower bound. You can do this in one of two ways (or both): Find the variance analytically (you'll need the gamma MGF) and comparing it to the bound you derived above, or Approximate the variance of o, numerically via Monte Carlo at several different values of 0, then plot both the lower bound you derived above and your Monte Carlo approximations on the same graph; take a fixed value of n, say, n = 10.