Problem #01 (8 points). Let Y,Y, ,Y be a random sample from the exponential distribution with pdf as follows (a) (4 points) Show that @ = Y is a consistent estimator of e. (b) (4 points) Obtain the maximum likelihood estimator for 0. Problem # 02 (6 points): Let Y,Y, ..,Y be a random sample from a normal distribution with unknown mean u and known standard deviation o . The pdf of Y is given as follows f( |AG,)= 1 J. V/2x Show that n is an MVUE for the parameter u(/-3) Problem #03 (8 points): Let Y,Y, ,Y, denote independent and identically distributed random variables from the following probability density function 2y 8 Osys- otherwise (a) (4 points) Find the method-of-moment estimator for e. (b) (4 points) Find the sufficient statistic for e