Theory of Statistics

Let Y1, . . . , Yn be i.i.d. samples from the density).r function 1 _ _ : f9(y) = 5""ij 1'3 y {61930,y30- Here 1" > 0 is a known positive constant. (a) Find the uniformly most powerful test for testing Ho : t9 = 30 versus H1 : 3 > (90. (b) Using the central limit theorem, give an approximate analytic expression for the critical value of the above test