Question: 1. Let (X 1,X2, . . . , X) be a random sample from N (,u, 02). Find the generalized likelihood ratio test of Ho

$1. Let (X 1,X2, . . . , X\") be a$

1. Let (X 1,X2, . . . , X\") be a random sample from N (,u, 02). Find the generalized likelihood ratio test of Ho : 02 : 03 vs H1 : 02 7 03 for each of the following two cases: (a) ,u = no is known. Soln: It can be shown that A = "rt" exp(n/2)T\"/2 exp(T/2), where T = 221:1 (X i \"(1)2 / 0%, which follows 3 X201) under H 0. The critical region for the GLRT test is given by A Cg for some 0

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