16. The UMP unbiased tests of the hypotheses HI' " '' H4 of Theorem 3 are unique if attention is restricted to tests depending on U and the T 's.

#!#17. Let X and Y be independently distributed with Poisson distributions P(A) and P(p.). Find the power of the UMP unbiased test of H: Po 5 A, against the alternatives A = .1, Po = .2; A = 1, Po = 2; A = 10, Po = 20; A = .1, Po = .4; at level of significance a = .1. [Since T = X + Y has the Poisson distribution P(A + Po), the power is 00 (A+)I fJ=LfJ(t) Po - (>..+1') 1-0 t! e , where fJ( t) is the power of the conditional test given t against the alternative in question.]