Document Type

Article

Publication Date

2-2007

Abstract

Let t⩾0. Select numbers randomly from the interval [0,1] until the sum is greater than t . Let α(t) be the expected number of selections. We prove that α(t)=et for 0⩽t⩽1. Moreover, . This limit is a special case of our asymptotic results for solutions of the delay differential equation f(t)=f(t)-f(t-1) for t>1. We also consider four other solutions of this equation that are related to the above selection process.

Publication Title

Expositiones Mathematicae

Volume

25

Issue

1

First Page

1

Last Page

20

Required Publisher's Statement

Copyright © Elsevier B.V

This is the authors' post print version of the paper, the published version can be found at the links below.

doi:10.1016/j.exmath.2006.01.004

http://www.sciencedirect.com/science/article/pii/S0723086906000053

Included in

Mathematics Commons

Share

COinS