situation. Suppose X1,..., Xn ~ N(μ1,02) and Y₁,..., Xm d N(μ2, σ²) are all independent, and we'd like to test Ho μ1 =μ2. Let A(0; D) denote the likelihood ratio-here, evaluated on the set o D= {X1, Xn, Y₁, ..., Ym}. = {(μ1, μ2) μ₁ = μ2} CR2 and for (a) Briefly state the answers to the following questions: (i) What are the MLES of μ1, M2, σ² under the current model assumption? (ii) What are the MLES of μ1, M2, 02 while being restricted to the set no? (b) Show that 2 log A(No; D) = (n + m) log [1 + nm(X-Y)²] (n+m)S² where + Xn Y₁₁ + ...+Ym X n m n m , and_S² = Σ(X; – X)² + Σ(Ÿ¿ − Ÿ)². i=1 j=1 [Hint: You can use the fact that, given a set of numbers {1,..., zn} and their average z = identity (-a)² = ²²±1(i − )² + n(ž− a)² holds for any a.] - (21+ +zn)/n, the