A STOCHASTIC-PROCESS ARISING IN SEQUENTIAL EXPERIMENTATION

Abstract

Experiments are launched at every time instant n is an element of Z, the times until completion being i.i.d. non-negative random variables X(n). We consider the process formed by the temporally ordered completion times. Formulas for its one- and two-dimensional marginal distributions are derived from which we obtain closed-form expressions for these distributions as well as for the inter-arrival time density in the case of exponential X(n).