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

Marc Mignolet, Chung Chih Lin

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

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.

Original language English (US) 65-74 10 Probabilistic Engineering Mechanics 7 2 https://doi.org/10.1016/0266-8920(92)90010-F Published - 1992

random variables
Random variables
moments
intervals
thresholds
simulation

### ASJC Scopus subject areas

• Mechanical Engineering
• Safety, Risk, Reliability and Quality

### Cite this

In: Probabilistic Engineering Mechanics, Vol. 7, No. 2, 1992, p. 65-74.

Research output: Contribution to journalArticle

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