Evaluating Best-Case and Worst-Case Variances When Bounds are Available

Abstract

This paper describes procedures for computing the tightest possible best-case and worst-case bounds on the variance of a discrete, bounded, random variable when lower and upper bounds are available for its unknown probability mass function. An example from the application of the Monte Carlo method to the estimation of network reliability illustrates the procedures and, in particular, reveals considerable tightening in the worst-case bound when compared to the trivial worst-case bound based exclusively on range.