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Suppose that X1, ..., Xn are iid with a beta(#, 1) pdf and Y1, ..., Ym are iid with a beta(0, 1) pdf. Also assume

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Suppose that X1, ..., Xn are iid with a beta(#, 1) pdf and Y1, ..., Ym are iid with a beta(0, 1) pdf. Also assume that the Xs are independent of the Ys. (a) Find an LRT of Ho : 0 = u versus H1 : 0 # H. (b) Show that the test in part (a) can be based on the statistic T = Elog Xi Elog Xi + Elog Yi (c) Find the distribution of T when Ho is true, and then show how to get a test of size a = .10

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