Let X = (X1, ..., Xn) be a collection of independent and identically distributed random variables with probability density function: f (2c; M, d ) = (20 - 1 ) 2 2723 exp x > 0, 2 2 x where u > 0, and > > 0. The mean and variance of this distribution are E(Xi) = M, Var(Xi ) = 1S (a) Calculate the maximum likelihood estimators of the parameters / and 1. [4] (b) Calculate the Fisher information matrix of (M, )). [8] ( c) Calculate the Jeffreys prior of (M, )). [4] (d) Is the maximum likelihood estimator of u a minimum variance bound unbiased estimator (MVBUE)? Justify your answer. [4]