Statistics questions

Let X1, X2, …, X,,, be independent Uniform(0, 0 + 1) distributed random variables. 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 naïve test which rejects the null if X1 > 1— a. Use your calculation to show that the power of the former is indeed larger.