full step please

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 5X1 - 2X2 2X1 + 3X3 - 2X H2 = - Xit=X, HA = m m N 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, 12, 13 and /4. Justify your answer. If the random sample consists of 3 independent observations X1, X2 and X follow Binomial distribution Binomial(4, p) consider following estimators for p : 3X1 - 2X2 P1 = Pz = X = X1+X2 + X3 PA = 7 X1 + X2 + X3 (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 Pi, P2, P3 and p4- Justify your