On the moments of random variables uniformly distributed over a polytope

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.

Keywords

• uniform distribution
• rth moment
• polytope.