Let X,..., X., be a random sample from the density 01.24. 10.1)(I), and let Y,...,Y, be a random sample from the density 62y92'Ion(y). Assume that the samples are independent. Set U. log, X;, i= 1,..., M1, and V, = log Y,, j = 1,..., 1 (a) Find the generalized likelihood-ratio for testing Ho : 0, = 0, versus H. : 817 82 (b) Show that the generalized likelihood-ratio test can be expressed in terms of the statistic T SU,+DV, (C) If H, is true, what is the distribution of T? (You do not have to derive it if you know the answer.) Does the distribution of T depend on er = , given that H, is true? Let X,..., X., be a random sample from the density 01.24. 10.1)(I), and let Y,...,Y, be a random sample from the density 62y92'Ion(y). Assume that the samples are independent. Set U. log, X;, i= 1,..., M1, and V, = log Y,, j = 1,..., 1 (a) Find the generalized likelihood-ratio for testing Ho : 0, = 0, versus H. : 817 82 (b) Show that the generalized likelihood-ratio test can be expressed in terms of the statistic T SU,+DV, (C) If H, is true, what is the distribution of T? (You do not have to derive it if you know the answer.) Does the distribution of T depend on er = , given that H, is true