(a) Let X,, X,,..., X be a random sample from the distribution f (x) =0 le-x10 ", x>0. (i) Show that the likelihood ratio test of H. :0=0, versus H, :0 #0, is based upon the statistic Y = X . Show that the rejection region is of the form Y SC, or Y ZC2. (ii) For 0. = 4 and n = 100, find the approximate significance level of the test that rejects H. if Y $3 or Y 2 5. Use the Central Limit Theorem. Is continuity correction needed? (iii) Use the rejection region in (ii) to find the power of the test when 0 = 4.5 and n = 100