Find the Bayes test to choose between the hypotheses, (H_{0}) and (H_{1}), whose prior probabilities are (frac{5}{8})

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Find the Bayes test to choose between the hypotheses, \(H_{0}\) and \(H_{1}\), whose prior probabilities are \(\frac{5}{8}\) and \(\frac{3}{8}\), respectively, when under \(H_{0}\) the datum \(x\) had the PDFimage text in transcribed

\(x\) always being positive. Let the relative costs of the two kinds of errors be equal. Find the minimum average probability of error.

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