2. Let Y be a random variable with distribution N(M, 1). Let X = e . Then X is said to have a lognormal distribution. (a) Show that the PDF of X is fx (20 ) = e - 2 (Inx - 1 )2, x >0. (b) Let X1, ..., Xn be a random sample from the above lognormal distribution. Find the method-of-moments estimator, u, of u (based on the distribution of X). (c) Let X1, ..., Xn be a random sample from the above lognormal distribution. Find the maximum likelihood estimator, u, of u (based on the distribution of X). (d) Compare the two estimators in terms of the unbiasedness. Hint: You may use Jensen's inequality, in particular, if Z is a non-degenerate random variable then E[In Z]