Central Limit Theorem

The central limit theorem (CLT) is, along with the theorems known as laws of large numbers, the cornerstone of probability theory. In simple terms, the theorem describes the distribution of the sum of a large number of random numbers, all drawn independently from the same probability distribution. It predicts that, regardless of this distribution, as long as it has finite variance, then the sum follows a precise law, or distribution, known as the normal distribution.

Let us describe the normal distribution with mean μ and variance σ2: It is defined through its density function,

where the variable x ranges from −∞ to +∞. This means that if a random variable follows this distribution, then the probability that it is larger than a and smaller than b is ...