Let X1, X2, …, X,,, be independent Uniform(0, 0 + 1) distributed random vari-ables. For testing Ho : 0 = 0 vs H1 : 0 > 0. 1. Find the level a uniformly most powerful test. (18 points) 2. Calculate its power and compare it with the power of a naive test which rejects the null if X1 > 1— a. Use your calculation to show that the power of the former is indeed larger.
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