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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 

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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