A variation of the Newton–Pepys problem and its connections to size-estimation problems

Abstract

This paper considers a variation of the 17 th century problem commonly known as the Newton-Pepys problem, or the John Smith's problem. We provide its solution and interpret the result in terms of maximum likelihood estimation. In addition, we illustrate the practical relevance of these findings for solving size-estimation problems, and in particular for determining the number of agents in a wireless sensor network.

Classic Problems of Probability–A Book Review

“…Gorroochurn takes care to note that, while Pepys originally posed the problem in terms of an exact number of sixes, Newton pointed out that "in reading the Question it seemed to me at first to be ill stated," and he therefore changed it to "at least one six." It is interesting to note that a variation on this old problem has recently been applied to size-estimation problems (see Varagnolo et al [17]).…”