Question: 38. Let Xl ' Xm ; Yl , ... , y be independently, normally distributed with means E and 1/, and variances a2 and

38. Let Xl" ' " Xm ; Yl , ... , y" be independently, normally distributed with means E and 1/, and variances a2 and 'T 2 respectively, and consider the hypothesis H:'T S a against K: a < 'T. (i) If E and 1/ are known, there exists a UMP test given by the rejection region E( lj - 1/)2/E( X; - E)2 C. (ii) No UMP test exists when Eand 1/ are unknown.

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