Theory of Statistics

Suppose Y1, . . . ,Yn are i.i.d. Poisson(/\\). Consider the testing problem: HuzAon vs H1:)\\7)\\43. (a) Find the uniformly most powerful test for testing Ho : t9 = (90 versus H1 : (9 > 6'0. (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 31 > 60, compute analytically the power function of the test in (a) at 61)