Problem 3. [5 marks] Consider linear model y = XB + e with E(E) = 0 and Var(e) = 02V where V is a known symmetric positive definite matrix. The ordinary least squares estimator (LSE) for 3 is 3. = (X X)-1Xy, and the generalized least squares estimator (GLSE) is B. = (X V-1X)-1XTV-ly. (3a) [1 mark] Show that the GLSE B, is an unbiased estimator for B. (3b) [1 mark] Show that V (B,) = 02(XTV-1X)-1. (3c) [1 mark] What is the advantage of the GLSE over the LSE? No need to explain. (3d) [1 mark] When do we call the GLSE a weighted least squares estimator (WLSE)? (3e) [1 mark] What is the function S(B) that the WLSE minimizes