Random arcs on the circle-Reference-Cited by-同舟云学术

Random arcs on the circle

Published:1978-12 Issue:04 Volume:15 Page:774-789
ISSN:0021-9002
Container-title:Journal of Applied Probability
language:en
Short-container-title:J. Appl. Probab.

Author:

Siegel Andrew F.

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.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference10 articles.

1. Covering the circle with random ARCS

2. On the Measure of a Random Set

3. The Random Division of an Interval and the Random Covering of a Circle

4. SOLUTION TO A GEOMETRICAL PROBLEM IN PROBABILITY

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