Vol. 54, No. 2, 1974

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Random points in a simplex

William John Reed

Vol. 54 (1974), No. 2, 183–198
Abstract

The expected values of certain functions of N points chosen at random in an n dimensional simplex or paraUelotope are considered, and a decomposition of such integrals is obtained by use of a generalised form of Crofton’s Theorem.

Explicit expressions are found for the moments of the area of the triangle formed by three points chosen at random in a triangle or parallelogram.

Mathematical Subject Classification 2000
Primary: 52A25
Secondary: 60D05
Milestones
Received: 6 December 1972
Published: 1 October 1974
Authors
William John Reed