Mathematics Commons^™

An Unexpected Limit Of Expected Values, Branko Ćurgus, Robert I. Jewett

Mathematics Faculty Publications

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.