4. Let Xi....,X, be independent and suppose that E(X,) = k,0 + bi, for known constants /; and bi, and Var(Xi) =o' , i= 1, . . . ,n. (a) Find the least squares estimator 0 of 9. (b) Show that / is unbiased. (c) Show that the variance of 0 is Var(0) =,?, (d) Show that E(x, -ke -b)?= >(x -ke -b)?+ 24(0-0) i=1 im1 i=1 [3] (e) Hence show that E E(x, -ke-b)? = (n - 1)o' [2]