Coupon Collector Problem: Part 1

This lecture covers the coupon collector problem, where balls are thrown independently and uniformly at random into bins. The goal is to determine the minimum number of balls needed to ensure each bin contains at least one ball. The lecture discusses the expected behavior, defines Tk as the first time k bins are occupied, and analyzes the probability distribution of X = Tn. The Erdős-Rényi proposition is introduced, relating to the Gumbel distribution and the behavior of Tn in terms of n and log n. The lecture concludes with implications of large positive and negative values of G in the context of the coupon collector problem.