Problem 1 (25 points). Let X1, X2, ... bei.i.d. variables uniformly distributed on (0, 20), and A >0 is the unknown parameter. Define G, and H, as follows: Gn = (X1 X X2 X . . . xX )l n Hn = X+ . . . +X, (1) (15 points) Find the constant c and c2 such that On = c1 . Gn and On = c2 . Gn are both consistent estimators of 0. (2) (10 points) Find the maximum likelihood estimator , of d and show that the M.L.E. is a consistent estimator of 0