Problem 1: Suppose we observe a random variable X having the density S020-1 fx(x; 0) = if 0 < x < 1 otherwise, where 0 > 0. (a) What is the critical region for the likelihood ratio test of Ho : 0 = 1 against H₁ : 0 = 2 at level of significance a = 0.05? (b) What is the power of the likelihood ratio test in part (a)?

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