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An Unexpected Limit of Expected Values
Expositiones Mathematicae
  • Branko Ćurgus, Western Washington University
  • Robert I. Jewett, Western Washington University
Document Type
Article
Publication Date
2-1-2007
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.
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/