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The random volume of interpenetrating spheres in space

Published online by Cambridge University Press:  14 July 2016

P. A. P. Moran
P. A. P. Moran*
Affiliation:
The Australian National University, Canberra
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Abstract

The distribution of the volume occupied by random spheres in a cube is considered, both when the number of spheres is fixed and when their centres form a Poisson field. The mean and variance are obtained and in the latter case the distribution is proved to converge to normality. The probability of complete coverage is also obtained heuristically.

Keywords

GEOMETRICAL PROBABILITYCOVERAGEINTERPENETRATING SPHERES
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 483 - 490
Copyright
Copyright © Applied Probability Trust 1973 

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References

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