18. (i) Let Xl' . . . ' Xn be a sample from the uniform distribution V(O, 8), o< 8 < 00, and let T = max(Xl' ... , Xn ) . Show that T is sufficient, once by using the definition of sufficiency and once by using the factorization criterion and assuming the existence of statistics 1'; satisfying (17}-(19). (ii) Let Xl' . . . ' X; be a sample from the exponential distribution E(

a, b) with density (l/b)e -(X-a)/b when x a (-00 < a < 00, 0 < b). Use the factorization criterion to prove that (min(X1,... , Xn ) , E7-1X;) is sufficient for

a, b, assuming the existence of statistics 1'; satisfying (17}-(19) .