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Under H0 , a random variable has the cumulative distribution function F0 (x) = x2 , 0 ≤ x ≤ 1; and under H1 it has the cumulative distribution function F1(x) = x3, 0 ≤ x ≤ 1.
(a) If the two hypotheses have equal prior probability, for what values of x is the posterior probability of H0 greater than that of H1?(b) What is the form of the likelihood ratio test of H0 versus H1?(c) What is the rejection region of a level α test?(d) What is the power of the test?
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