These are the question please answer asap

Problem 1. (40 points). Let X1, X2, ... X, denote a random sample from a population having mean / and variance o'. Consider the following estimators of /: Xi + X2+ ... + XT and 92 = 2X1 - X6+ X4 + 3X5 5 a. (10 points). Is either estimator unbiased? Justify your answer. b. (10 points). Compute the variance of each estimator. c. (10 points). Which estimator is better? In what sense is better? Justify. d. (10 points). A realization for the experiment gave the following readings: 21 = 2.3, 12 = 3.4, 13 = 1.8, CA = 2.7, x5 = 1.5, $6 = 2.4, and my = 3.2. Compute estimates for a using both the estimators defined above.Problem 2. (35 points). Let X be a random variable with the following pdf f (I) = (@+ 2)10+1 , if0