Problem 5. Let X1, . . . ,Xm and Y1,. ..,Y,., he independent samples from two normal populations with 2 2 unknown means m and H2 and unknown variances of and :13. Consider testing Hg : 01 = or? versus H.I : of % erg. (1) Derive the LR test statistic A. (2) Show that the rejection region of the LRT is of the form {R b} with % 22-1109 ' 2:12 % 2321(1); _ Y)2 (3) What is the distribution of R under the null hypothesis? R