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A more general form of a theorem of Crofton

Published online by Cambridge University Press:  14 July 2016

H. Ruben  and
W. J. Reed
H. Ruben
Affiliation:
McGill University, Montreal
W. J. Reed*
Affiliation:
McGill University, Montreal
*
*Now at the University of British Columbia, Vancouver.
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Abstract

Let Dj be a domain in nj,-dimensional Euclidean space, for j = 1, …, k. Suppose that for each j = 1,…, k, Nj points are chosen independently at random in Dj. A theorem, which is an extension of a theorem of Crofton, is proved about the expected value of functions of the points.

Keywords

GEOMETRIC PROBABILITYCROFTONRANDOM POINTSSYLVESTERS PROBLEM
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 479 - 482
Copyright
Copyright © Applied Probability Trust 1973 

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Footnotes

Research largely carried out at McGill University as part of an M. Sc. thesis.

References

[1] Crofton, M. W. (1885) Probability. Encyclopaedia Britannica. Ninth edition, 19, 768–788.Google Scholar
[2] Williamson, Benjamin (1887) An Elementary Treatise on the Integral Calculus. Second Edition. Longmans, Green and Co. London. Chapter XI, 298–340.Google Scholar
[3] Miller, W. J.C. (1863) Editor, series of mathematical questions and solutions, published in Educational Times , London. Also published as Mathematical Questions and their Solutions from the Educational Times. (1864–1901) London.Google Scholar
[4] Reed, W. J. Random points in a simplex. To appear.Google Scholar
[5] Kendall, M. G. and Moran, P. A. P. (1963) Geometric Probability. Griffin, London.Google Scholar