3. [15 points] Let X1,..., Xn ~iid Unif(0, 0). We wish to test Ho: 0 = 1 vs H: 01. Recall that the MLE is the sample maximum T = X(n), and the sampling distribution is / ~Beta(n, 1) which has a CDF of F(x) = x for 0 < x < 1. (a) Write our the likelihood ratio test statistic A(X) in terms of T. (Be sure to consider both the case when T < 1 and when T > 1.) (b) Show that this will give the rejection region R = {T < c or T > c2}, and find the necessary values of c and c2 for the test to be size a. (c) Could you alternatively build an c2? Why or why not? an asymptotic LRT to avoid determining the values of c and