Assume the service time of a customer at a store follows a Pareto distribution with minimum waiting time equal to 0 minutes. The maximum length of the service is dependent on the type of the service. Suppose X1, X2, . . ., X, is a random sample of service times of n customers, where each X; has a Pareto density given by fo(x) = [40x* 40x-5, x 0, 0, x < 0. for an unknown 0 > 0. a. Find a sufficient statistics for 0. (4 pts) b. Call it sufficient statistics, T(X) = . Find the MVUE of 0. (4 pts) c. Show that is a pivotal quantity. Using this pivotal quantity, derive a statistics 1 L such that P (L < ) = 0.9. (4 pts) d. Find the method of moments estimator of 0. Is the method of moments estimator consistent? Fully justify your answer. (4 pts)