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The Volume of a Tetrahedron whose Vertices are Chosen at Random in the Interior of a Parent Tetrahedron

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

David Mannion
David Mannion*
Affiliation:
Royal Holloway College
*
* Postal address: Department of Mathematics, Royal Holloway College, University of London, Egham, Surrey, TW20 0EX, UK.
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Abstract

We solve a problem proposed by V. Klee (1969). He asked for a calculation of κ, the expected value of V, the volume of a daughter tetrahedron whose vertices are chosen at random (i.e. independently and uniformly) in the interior of a parent tetrahedron of unit volume. We discover:

We also calculate the second, fourth and sixth moments of V.

Keywords

KLEE'S PROBLEMSYLVESTER'S PROBLEMVOLUME OF RANDOM TETRAHEDRONVOLUME OF RANDOM SIMPLEXRANDOM APPROXIMATION OF CONVEX SETSCONVEX HULL

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 26 , Issue 3 , September 1994 , pp. 577 - 596
Copyright
Copyright © Applied Probability Trust 1994 

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