For given real and monotone functionshi's, we obtain the necessary and sufficient conditions in order that any n-valuated function[Psi](x) be the conditional expectationE(h(X)/X>x) of a discrete random vectorX, whereh(X) denotes the random vector (h1(X1), ..., hn(Xn)).

The purpose of this paper is to give conditions on the parameters of nonhomogeneous Poisson and nonhomogeneous pure birth processes, under which the corresponding random vector of the first n epoch times has some multivariate stochastic properties. These results provide an inside to understand...