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On the distribution of a random triangle

Published online by Cambridge University Press:  14 July 2016

V. S. Alagar
V. S. Alagar*
Affiliation:
Concordia University, Montreal
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Abstract

In this paper we find the distribution of the area X of a randomly chosen triangle within a given triangle T. An extension of the classical Crofton technique is used in setting up a sequence of differential equations to obtain the desired distribution.

Keywords

RANDOM TRIANGLECONVEX HULLMOMENTSDISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 284 - 297
Copyright
Copyright © Applied Probability Trust 1977 

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References

Alagar, V. S. (1975) The Distribution of the Volume of Random Sets and Related Problems on Random Determinants. , McGill University, Montreal, Canada.Google Scholar
Klee, V. (1969) What is the expected volume of a simplex whose vertices are chosen at random from a given convex body? Amer. Math. Monthly 76, 286–288.Google Scholar