1. Let (X1, X2, ..., Xn) be a random sample from an exponential distribution with probability density function f(x) given by , for r > 0; f(I) = 0, otherwise. (a) Find the moment estimator A of 1. (b) Show that A is a biased estimator of A for a finite sample of size n, but becomes unbiased as n -> co. Hint: You should be able to find the exact distribution of 1/1.] (c) Modify the moment estimator A to provide an unbiased estimator of A, namely AMod