Convergence of unforced errors in the matching problem

The Central Limit Theorem (CLT) is a fundamental result in probability theory with numerous applications in various disciplines. There are a wide variety of CLT‐like theorems, for example the De Moivre–Laplace, Lindeberg and Lyapounov theorems. Independent and identically distributed random variables with a finite second moment are usually considered assumptions in CLTs. However, in this article we present a CLT for a sum of dependent and nonidentically distributed Bernoulli random variables that arises in the well‐known matching experiment.