Longest Waiting Time in the Coupon Collector’s Problem
C. Brennan *
The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa.
J. Kariv
School of Statistics and Actuarial Science, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa.
A. Knopfmacher
The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa.
*Author to whom correspondence should be addressed.
Abstract
The coupon collector’s problem is a classical problem usually solved by summing independent but not identically distributed geometric random variables. These geometric random variables represent waiting times for the j-th coupon for j = 1, 2,..... In this paper we address the question about the longest of these waiting times. In particular, we evaluate the moments of the longest waiting time.
Keywords: Coupon collectors problem, maximum, moments