Let X1, X2, ....X, be independent Uniform(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 X] > 1-a. Use your calculation to show that the power of the former is indeed larger. (7 points)