#### 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)=e^{t} 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

#### Recommended Citation

Ćurgus, Branko and Jewett, Robert I., "An Unexpected Limit of Expected Values" (2007). *Mathematics.* Paper 70.

http://cedar.wwu.edu/math_facpubs/70