1. Let (X1, X2, ..., Xn) be a random sample from an exponential distribution with probability density function f(x) given by Ae-" for x > 0; f (ac) = 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 ) to provide an unbiased estimator of 1, namely AMod.4. Let (X1, X2, . . . ,Xn) be a random sample from a binomial (r, 10) distribution where both 1" and p are unknown. (a) Find the moment estimators of r and p. (b) Use the estimators in (a) to estimate 1" and 3) using the following observed sample (note that 7' should be rounded off to the nearest non-negative integer): 21, 24., 19, 25, 24, 22, 22, 19, 20, 23