Consider two independent samples, X1, . . . , Xm from a N(1, ^2 1 ) distribution and Y1, . . . , Yn from a N(2, ^2 2 ) distribution

Problem 3. Consider two independent samples, X1, . . . ,Xm from a N(p.1, a?) distribution and Y1,...,Yn from a N 010,03) distribution. Here #1, #2, (Ti? and 02 are unknown. Consider testing the null hypothesis that the two population variance are equal, H 0 : of = 0%, against the alternative that these variances are different, H1 : 0% 3% 03. (1) Derive the LR test statistic A. (2) Show that the rejection region {A b} with 22210? Y)2/(n 1) and a