Article
An Unexpected Limit of Expected Values
Expositiones Mathematicae
Document Type
Article
Publication Date
2-1-2007
Keywords
- Linear delay differential equations,
- Asymptotic behavior,
- Sums of independent random variables,
- Random walks
Disciplines
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.
DOI
http://dx.doi.org/10.1016/j.exmath.2006.01.004
Subjects - Topical (LCSH)
Differential equations, Linear; Asymptotic distribution (Probability theory); Random walks (Mathematics); Random variables
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf
Citation Information
Branko Ćurgus and Robert I. Jewett. "An Unexpected Limit of Expected Values" Expositiones Mathematicae Vol. 25 Iss. 1 (2007) p. 1 - 20 Available at: http://works.bepress.com/branko_curgus/20/