Question: 5. An experiment was devised to test whether the parameter A of a sample from the density f (y) = A2ye'Ay, y > 0 is

5. An experiment was devised to test whether the parameter A of a sample from the density f (y) = A2ye'Ay, y > 0 is equal to a believed value A0 = 50. (a) Derive the most powerful test for the null hypothesis H0 : {A = A0} vs alternative hypothesis Ha : {A = A3} for A(1 2 40. (b) Discuss whether this test is uniformly most powerful to test against a composite alternative Ha : {A

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