Problem 6: Let X1, ..., Xn be i.i.d random variables, each with probability mass function O k if k = 1, 2, 3, P(X = k) = otherwise, where k are unknown parameters such that 0 2 0 and 01 + 02 + 03 = 1. Equivalently, the probability mass function for each X; can be written as Px (x; 01, 02, 03) = 01(2=10)(2=2101(x=3) _ 01(*=10)(x=2)(1 -01 -02) 1(2=3). Here 1{ } is an indicator function, which equals 1 if the event inside { } happens and equals 0 otherwise. Let n, be the number of observations for outcome k, k = 1, 2,3. So ni + n2 + n3 = n. Test Ho : 01 = 02 = 03 against H1 : 01, 02, 03 are not all equal. Use Wilks' Theorem to derive the critical region of the generalized likelihood ratio test at the significance level a