see attached 3

3 (10 pts) A researcher is going to determine the estimators of parameters 61 and 92 by maximizing the expression l(6|X1----Xn) = %ln27r glng 2%02 . :- (Xz' 91)2. The estimator will be applied with the random sample X1....Xn. a) Write the probability density function which characterizes the population from which the random sample comes. Is it a well known density? b) Find the estimators for parameters 91 and 92, explaining the steps that you follow. 6) Is it 32 unbiased? Is it g consistent? Explain. d) Do we have another method to derive estimators for 6'1 and 62? Please apply. Do we get the same estimators? e) Now assume that X1....Xn is a random sample from a population with X N U(0, 6). Find the Method of Moments estimator for 6. f) Show that the MLE estimator is 3 = max{X1....Xn}, diiferent from the MM esti- mator