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4. (35 points) Let X1, X2, . .. , Xn be iid sample from N(0, o2) where of is unknown. We want to test the following: Ho : 02 =09 vs H1: 02 > 09. (a) (10 points) Let us write S2 = 1 En, X?. Show that the likelihood ratio is given by LR = exp z (1 - 8:) ] if $2 2 08 if $2