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Q3Section I (Objective (Q1–Q80))3 of 80

Statistical Inference — checking a randomized most powerful test

Let X be a random variable with pmf under H0H_0 and H1H_1 given by: for X=1,...,6, pθ0(x)=0.01,0.01,0.01,0.01,0.01,0.95p_{\theta_0}(x)=0.01,0.01,0.01,0.01,0.01,0.95 and pθ1(x)=0.05,0.04,0.03,0.02,0.01,0.85p_{\theta_1}(x)=0.05,0.04,0.03,0.02,0.01,0.85. Consider a test function φ(x)\varphi(x) as 11 if X=1,2X=1,2; 0.250.25 if X=3X=3; 00 otherwise. Then which one of the following is correct?

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