1. Suppose that Yl, ..., Y, is a sample of size n = 10 from a Exp(@), with pdf f (y; 0 ) = exp { - / } , 0 >0, y>0. (a) Suppose you would like to test Ho : 0 = 2 versus H. : 0 = 1 at the significance level 0.05. Derive the critical region of most powerful test for this testing situation. (b) Derive the power of the test given in a). (c) Suppose that we observe _ y; = 12. Is there enough evidence to reject Ho at the significance level o = 0.05? (d) Find the ML estimator of 1/P(Y, > 1.5)