4. Let X1, X2, . . . , Xn be independent exponentially distributed random variables with mean 1/.

(a) [4 points] Show that S = min{X1, X2, . . . , Xn} has an exponential distribution with parameter n.

(b) [4 points] Find an unbiased estimator of 1/ that can be written in terms of S.

(c) [4 points] Let T be the unbiased estimator found in part(b). Find the mean squared error (MSE) of T and compare it with the MSE of the sample mean X = 1 n Pn i=1 Xi .(Hint: use the result of part(a).)