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The number of intersections of random chords to a circle — third and fourth moments

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 St., London SE18 6PF, U.K.
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Abstract

In this paper the distributions of the number of intersections of three, four and five random chords to a circle are obtained by a reduction technique employing Ptolemy's theorem. These results are then used to obtain the skewness and kurtosis of the number of intersections of n random chords to a circle.

Keywords

RANDOM CHORDSINVARIANT LINE DENSITYSKEWNESS AND KURTOSIS OF INTERSECTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 355 - 372
Copyright
Copyright © Applied Probability Trust 1982 

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References

[1] David, F. N. and Fix, E. (1964) Intersections of random chords of a circle. Biometrika 51, 373–379.Google Scholar
[2] Janson, S. (1978) On random divisions of a convex set. J. Appl. Prob. 15, 645–649.Google Scholar
[3] Santalo, L. A. (1976) Integral Geometry and Geometrical Probability. Addison-Wesley, Reading, MA.Google Scholar
[4] Solomon, H. S. (1978) Geometric Probability. SIAM, Philadephia, PA.Google Scholar
[5] Sulanke, R. (1965) Schnittpunkte zufälliger Geraden. Arch. Math. 16, 320–324.Google Scholar