A History of the Central Limit Theorem

Abstract

One of the most important theorems in statistical mathematics and probability theory is the Central Limit Theorem (CLT). It is used almost everywhere where statistical mathematics is applied. The usefulness of the theorem lies in its simple definition. The central limit theorem states that if some certain conditions are satisfied, then the distribution of the arithmetic mean of a number of independent random variables approaches a normal distribution as the number of variables approaches infinity. In other words, there is no need to know very much about the actual distribution of the variables, as long as there are enough instances of them their sum can be treated as normally distributed. The beauty of the theorem thus lies in its simplicity.