Problem 1 [22 points]: A random sample consists of 3 independent observations X1, X2 and X3 follow Normal distribution N(u, 2) consider four estimators for population mean H as follow: X1 + 3X2 - 2X3 5X - 2X2 2X1 + 3X3 - 2X A1 = 12 = 2 3 13 =X1+=X, H4= Where X is the sample mean of X1, X2, X3- (a) [4 points] Which of the above is/are the unbiased estimator(s) for u ? (b) [4 points] Which of the above is the best unbiased estimator for u ? (c) [3 points] Provide an estimator for u which is better than aforementioned /1, #2, 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 P2 = X = 1 X1+ X2+ X3 X X1+X2+X3 P1 = 4 P3 = =X1 X, P4 = = 3 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