Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T05:12:37.909Z Has data issue: false hasContentIssue false

A note on the volume of small random simplexes

Published online by Cambridge University Press:  14 July 2016

John Gates*
Affiliation:
Thames Polytechnic
*
Postal address: School of Mathematics, Statistics and Computing, Thames Polytechnic, Wellington Street, London SE18 6PF, U.K.

Abstract

This note shows how the initial density of the volume of a random simplex in a body, K, depends upon the fourth moment of sectional area and so rejects the conjecture that this initial density is independent of K.

Keywords

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1984 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Deltheil, R. (1926) Probabilités géométriques. Gauthier-Villars, Paris.Google Scholar
Henze, N. (1983) Random triangles in convex regions. J. Appl. Prob. 20, 111125.Google Scholar
Santaló, L. A. (1976) Integral Geometry and Geometrical Probability. Addison-Wesley, Reading, Ma.Google Scholar