Problem 2 40.0 points possible (graded, results hidden) Suppose that Zi = = xi 0 +i i with the () known and the (i ~ N (0, , 1)). (1) The weighted least squares estimator minimizes: (2 - ) (zi - Ox) (2 - ; 2/ (zi " (2; - 2 (2) Find the weighted least squares estimator . = n i1 Zixi/0 Zi=1 i=1 = = 1 Zixi/ n i-1 Zixi n _i=1 = -1 Zixi 1 (3) What is E (0)? (0) = 10/6 E () E () = 0 E () = = 10/0 i=1 10/0 an 1 xi/ i=1 (4) What is Var ()? Var () = Var () = 1 (12?/?? i-1 x (1 17/03 O Var (0) = 23/0 O 1 -1 x Var () = (5) What is the distribution of ? Normal Student-t Chi-squared Gamma