Problem 1 [22 points]: A random sample consists of 3 independent observations X1, X2 and X3 follow Normal distribution N(u, oz) consider four estimators for population mean u as follow: X1 + 3X2 - 2X3 5X - 2X2 2X1+ 3X3 - 2X 41 = 2 12 = 3 13 = Xit=x, 14 = 3 Where X is the sample mean of X1, X2, X3- (a) [4 points] Which of the above is/are the unbiased estimator(s) for M ? (b) [4 points] Which of the above is the best unbiased estimator for u ? (c) [3 points] Provide an estimator for / which is better than aforementioned /1, 12, 13 and 4. Justify your answer. If the random sample consists of 3 independent observations X1, X2 and X3 follow Binomial distribution Binomial (4, p) consider following estimators for p : 3X1 - 2X2 X1+X2+ X3 X X1+X2+ X3 P1 = P2 = X = - 4 3 P3 = 5X1 -7X, PA = = N 6 (d) [4 points] Which of the above is/are the unbiased estimator(s) for p ? (e) [4 points] Which of the above is the best unbiased estimator for p ? (f) [3 points] Provide an estimator for p which is better than aforementioned P1, pz, P3 and p4. Justify your