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A note on the volume of small random simplexes

Published online by Cambridge University Press:  14 July 2016

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

INITIAL DENSITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 651 - 653
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, 111–125.Google Scholar
Santaló, L. A. (1976) Integral Geometry and Geometrical Probability. Addison-Wesley, Reading, Ma.Google Scholar