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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 1, Pages 197-200
http://dx.doi.org/10.1155/S0161171297000240
Research note

On the moments of random variables uniformly distributed over a polytope

Department of Mathematics and Computer Science, The University of the West Indies, Trinidad and Tobago

Received 24 February 1995; Revised 8 May 1995

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Suppose X=(X1,X2,,Xn) is a random vector uniformly distributed over a polytope. In this note, the author derives a formula for E(XirXjs), (the expected value of XirXjs), in terms of the extreme points of the polytope.