Question: 2. Let (X1,X2, . . . ,Xn) be a random sample from X ~ exp()1), and (Y1,Y2, . . . ,Ym) be a random sample

2. Let (X1,X2, . . . ,Xn) be a random sample from X ~ exp()\\1), and (Y1,Y2, . . . ,Ym) be a random sample from Y N exp()\\2), X and Y are independent. (a) Find the generalized likelihood ratio statistic A for testing Ho : A1 = A2 vs H1 : A1 7E A2. (b) Show that the generalized likelihood ratio test @(X) can be expressed in terms of the statistic T = n ELI Xim . 21:1 Xi + 21:1 Yi (c) Find the exact distribution of T under H0, and specify the critical region of GLRT at level a. (d) Find the critical region of this test by using the asymptotic distribution of generalized likelihood ratio statistic, A

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