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Q5Section A (Section A)5 of 60

Power of an MP Bernoulli test

Let X1,X2,X3X_1,X_2,X_3 be i.i.d. Bin(1,θ)\mathrm{Bin}(1,\theta) random variables. Consider the problem of testing the null hypothesis H0:θ=12H_0:\theta=\frac12 against the alternative hypothesis H1:θ=14H_1:\theta=\frac14 based on X1,X2,X3X_1,X_2,X_3. Then the power of the most powerful test of size 0.1250.125 is

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