2. Let X1,X2, . . . ,Xn be an i.i.d. random sample from X. Assume that X has a density function given by f( ) at3'1, cc 2 1 1' : 0, a." 0 is an unknown parameter. (a) [3 points] Find the maximum likelihood estimator for 6. (b) [4 points] Find a 100(1 0:)% condence interval for 6. (c) [3 points] Show that. Tn = 3:21;] log X; is an unbiased estimator for %, i.e. E[T,.1] = %. (log denotes the logarithm with base 6.) (d) [6 points] 'What is the density of HT\"? (use the included MGF table)