Q6. Suppose that we have two independent random samples: X1, X2, . .., X,, are exponential(0) and Y1, Y2, . . ., Ym are exponential(/). Note that X ~ Exp()) when the pdf of X is f (x) = - exp (- * ) , 1 2 0 , I > 0 . (a) Find the LRT of Ho : 0 = / versus H1 : 0 / H. (b) Show that the test in part (a) can be based on the statistic T - EX+EY (c) Find the distribution of T when Ho is true