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Q2Section I (Objective (Q1–Q80))2 of 80

Statistical Inference — size and bias of a uniform critical region

Consider the distribution having probability density function of a random variable X as f(x,θ)=1θf(x,\theta)=\frac{1}{\theta}, 0≤x≤θ0\le x\le\theta; 00 elsewhere. Let 1≤X≤1.51\le X\le 1.5 be the critical region to test the hypothesis H0:θ=1.5H_0:\theta=1.5 against H1:θ=2H_1:\theta=2. Then

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