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On the moments of random variables uniformly distributed over a polytope. (English) Zbl 0876.62013
Summary: Suppose \(X= (X_1,X_2, \dots, X_n)\) is a random vector uniformly distributed over a polytope. In this note, the author derives a formula for \(E(X^r_iX_j^s \dots)\), (the expected value of \(X_i^rX_j^s \dots)\), in terms of the extreme points of the polytope.
MSC:
65C30 Numerical solutions to stochastic differential and integral equations
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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