5. [17 points] You observe n i.i.d. draws X1, . . . ,Xn from an unknown distribution and want to designing a hypothesis test to distinguish between two possibilities: 0 H0: X1, . . . ,Xn are drawn from a Uniform[0, 1] distribution. 0 H1: X1, . . . ,Xn are drawn from a Uniform\"), 2] distribution. (a) [5 points] Suppose you decide to perform a likelihood ratio test. Write an equation for the likelihood ratio LR as a function of the observed values X1 = 3:1, . . . ,Xn = as\". (b) [4 points] If n = 2 and you set the likelihood ratio threshold at c = 3, describe the set of values (:31, $2) for which you would choose H0 and the set of values ($1,332) for which you would choose H1. (c) [4 points] What is the Type I error of this test