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Random arcs on the circle

Published online by Cambridge University Press:  14 July 2016

Andrew F. Siegel
Andrew F. Siegel*
Affiliation:
University of Wisconsin-Madison
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Abstract

Place n arcs of equal lengths randomly on the circumference of a circle, and let C denote the proportion covered. The moments of C (moments of coverage) are found by solving a recursive integral equation, and a formula is derived for the cumulative distribution function. The asymptotic distribution of C for large n is explored, and is shown to be related to the exponential distribution.

Keywords

GEOMETRICAL PROBABILITYRANDOM ARCSRANDOM SETSCOVERAGEMOMENTS OF COVERAGEINTEGRAL EQUATIONVACANCY
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 4 , December 1978 , pp. 774 - 789
Copyright
Copyright © Applied Probability Trust 1978 

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