35. Random sample size. Let N be a random variable with a power-series distribution P(N = n) = a(n)An C(A) , n = 0,1, . . . (A > 0, unknown). When N = n, a sample XI"'" Xn from the exponential family (12) of Chapter 3 is observed. On the basis of (N, XI' " . , XN ) there exists a UMP unbiased test of H: Q(O):::;; c.