Question: 1. Let Xl' . . . X be a sample from the normal distribution N(t (1 2 ). (i) If 11 = 110 (known),

1. Let Xl' . . . • X" be a sample from the normal distribution N(t (1 2 ). (i) If 11 = 110 (known), there exists a UMP test for testing H: ~o against > ~o, which rejects when 1:(X; - ~o) is too large. (ii) If = ~o (known), there exists a UMP test for testing H: 11 110 against K : 11 > 110 , which rejects when1:(X; - ~0)2 is too large.

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