Mathematics · Statistical Inference
Let X1, X2 be a random sample from a population having a probability density function f ∈ {f0, f1} where: f0(x) = 1/2 if 0 ≤ x ≤ 2, and 0 otherwise; f1(x) = 1/4 if 0 ≤ x ≤ 4, and 0 otherwise. For testing the null hypothesis H0: f = f0 against the alternative hypothesis H1: f = f1, the power of a most powerful test of size α = 0.05 is equal to:
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