Let X1, X2, . .., X10 denote a random sample of size 10 from a Poisson distribution with mean 0. (a) Show that the critical region defined by _, x; 2 3 is a best critical region for testing Ho : 0 = 0.1 against H1 : 0 =0.5 (i.e. it corresponds to the most powerful test). (b) Determine, for this test, the significance level o (use quantities for the Poisson distribution). (c) Determine, for this test, the power at 0 = 0.5 (use quantities for the Poisson distribution)