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Q50Section C (Section C)50 of 60

Error probabilities of a uniform test

Let XX be a single observation drawn from U(0,θ)U(0,\theta) distribution, where θ∈{1,2}\theta\in\{1,2\}. To test H0:θ=1H_{0}:\theta=1 against H1:θ=2H_{1}:\theta=2 consider the test procedure that rejects H0H_{0} if and only if X>0.75X>0.75. If the probabilities of Type-I and Type-II errors are α\alpha and β\beta, respectively, then α+β\alpha+\beta equals __________ (round off to two decimal places)

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