Hypergeometric tail inequalities: ending the insanity

TL;DR

This paper surveys the hypergeometric distribution and discusses tail inequalities that provide bounds on the probability of deviations from the mean, offering insights into their applications and properties.

Contribution

It provides an informal survey of the hypergeometric distribution, highlighting key tail inequalities and their significance.

Findings

Clarifies the notation and symmetries of the hypergeometric distribution

Presents key tail inequalities with exponential bounds

Highlights the importance of these inequalities in probabilistic analysis

Abstract

The hypergeometric distribution is briefly and informally surveyed, including popular notation, symmetries, and the tail inequalities $Pr[i \ge E[i]+tn] \le e^{-2t^2n}$ and $Pr[i \le E[i]-tn] \le e^{-2t^2n}$.