Theory of Statistics

Let Y1, . . . ,Yn be i.i.d. samples from the density function 1 rl My) = 5m _ I" Q '9 y! 19>,y>0- (a) Find the uniformly most powerful test for testing Ho : f9 = 90 versus H1 : 9 > 30. (b) Using the central limit theorem, give an approximate analytic expression for the critical value of the above test. (c) Using (b), give an explicit approximate formula for the power function of the test in (a) for every alternative [i.e., for every alternative (91 > [90, compute analytically the power function of the test in (a) at 91)