Vol. 94, No. 2, 1981

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ISSN: 0030-8730
The volume cut off a simplex by a half-space

Leon Gerber

Vol. 94 (1981), No. 2, 311–314
Abstract

A formula for the volume cut off an n-dimensional simplex by a half-space has immediate application in probability theory. This note presents a derivation of such a formula in a short and completely elementary way and also yields the moments of this volume about the coordinate hyperplanes, and the volumes cut off the lower dimensional faces of the simplex and their moments.

Mathematical Subject Classification 2000
Primary: 52A25, 52A25
Secondary: 51M20, 53C65
Milestones
Received: 19 October 1979
Published: 1 June 1981
Authors
Leon Gerber