On the coupon-collector's problem with several parallel collections

TL;DR

This paper analyzes the expected time and variance to complete multiple parallel coupon collections when coupons arrive independently and uniformly, providing insights into the probabilistic behavior of such processes.

Contribution

It introduces a detailed evaluation of the expectation and variance for completing multiple parallel coupon collections under uniform independent arrivals.

Findings

Derived formulas for expectation and variance of waiting time

Quantified the variability in completion times

Enhanced understanding of parallel coupon collection dynamics

Abstract

In this note we evaluate the expectation and variance of the waiting time to complete $m$ parallel collections of coupons, in the case of coupons which arrives independently, one by one and with equal probabilities.