Statistics - Central limit theorem (CLT)
Table of Contents
1 - About
The central limit theorem (CLT) establishes that when random variables (independent) are added to a set their distribution tends toward a normal distribution (informally a “bell curve”) even if the original variables themselves are not normally distributed.
The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions.
The central limit theorem began in 1733 when de Moivre approximated binomial probabilities using the integral of <math>exp(-x^2)</math>. The central limit theorem achieved its final form around 1935 in papers by Feller, Lévy, and Cramér.
The central limit theorem is a fundamental component of inferential statistics
2 - Articles Related
3 - Example
3.1 - Galtonboard
Every ball is randomly pushed left and right. From http://galtonboard.com/
4 - Implementation
4.1 - Random Sample
The central limit theorem says that the averages of several samples obtained from the same population (ie a sampling distribution) following the central limit theorem rules (see below) will be distributed according to the normal distribution.