An Unexpected Limit of Expected ValuesExpositiones Mathematicae
AbstractLet 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.
Citation InformationBranko 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/