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On the lengths of the pieces of a stick broken at random

Published online by Cambridge University Press:  14 July 2016

Lars Holst
Lars Holst*
Affiliation:
Uppsala University
*
∗Postal address: Department of Mathematics, Uppsala University, Thunbergsvägen 3, S-752 38 Uppsala, Sweden.
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Abstract

Consider the pieces of a randomly broken stick. How long is the j th longest piece? How many breaks are necessary for getting all pieces less than a given length? These and related questions are studied in particular when the number of pieces is large. Using simple properties of the exponential distribution new proofs are given of old results and new results are obtained.

Keywords

SPACINGSUNIFORM DISTRIBUTIONEXPONENTIAL DISTRIBUTIONCOVERING A CIRCLEORDER STATISTICSLIMIT THEOREMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 623 - 634
Copyright
Copyright © Applied Probability Trust 1980 

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