Probability and conditional moments of multivariate uniform random variables satisfying a linear inequality constraint

A computational technique is presented to evaluate a class of probabilities and expectations of multivariate uniform random variables encountered in the analysis of certain random mechanical systems. First, a finite series representation is derived for the probability that a linear combination of n independent random variables uniformly distributed in the interval [0, 1] does not exceed a given threshold. This exact representation is then used to obtain closed from expressions for various moments, means in particular, of uniform random variables conditional on a linear inequality constraint. Finally, various practical implementation aspects of these computations are discussed and a comparison with the Monte Carlo simulation method is conducted that validates the use of the proposed technique.