A batch-ballot problem and applications

Abstract

Let (X1, X2, · ··, Xn) be a vector of discrete splittable and interchangeable random variables, and let Sj = Σji = 1Xi. This paper is concerned with probabilities of the form P{Sj < jb – d for j = 1, 2, 3, ···, n | Sn = r}. We focus on applications of these probabilities, study their properties and suggest how they may be computed. The applications are from the areas of computer science, economics, operations management, finance and risk theory.