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under h0 a random variable has the cumulative

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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