4.Suppose X1, X2, .., Xn is a random sample from lognormal with parameters / and o2. Then, by definition, Y1 = logX1, Y2 = logX2, ..., Yn = logXn are a random sample from N(u, o2) a. If o2 = 1, u is unknown, then use random sample Y1, Y2, ...Yn to derive the MLE of u. (The MLE estimator will be a function of Y's). Now plugin the formula for Yi = log(Xi) to write the estimator as a function of X1, X2, ..., Xn b. Jesus If 02 = 1, / is unknown. ( = Y = LET_, log(X;) is an estimator of A. What is the MSE of this estimator? (Hint: for unbiased estimators, MSE is the variance of the estimator) c. Suppose X follows log normal with parameters / = 2 and o2 = 1, then what is the mean and variance of X? Further what is the probability that X lies between 2.7 and 20.1