The central limit theorem refers to a kind of theorem in probability theory that discusses that the partial sum distribution of random variable sequences is asymptotic to normal distribution. This set of theorems is the theoretical basis of mathematical statistics and error analysis, and points out the conditions that a large number of random variables approximately obey normal distribution. It is the most important theorem in probability theory and has a wide practical application background.

In nature and production, some phenomena are influenced by many independent random factors. If the influence of each factor is small, the total influence can be regarded as obeying normal distribution. The central limit theorem proves this phenomenon mathematically. The earliest central limit theorem is the focus of discussion. In Bernoulli's experiment, the frequency of event A is close to normal distribution.

The history of central limit theorem;

The earliest central limit theorem is to discuss the asymptotic normality of the occurrence times of event A in N-fold Bernoulli test. Limit theorem is an important content of probability theory and one of the cornerstones of mathematical statistics, and its theoretical results are relatively perfect. For a long time, the analysis method of probability theory formed by the study of limit theorem has influenced the development of probability theory. At the same time, new limit theory problems are constantly emerging in practice.

The central limit theorem has an interesting history. The first edition of this theorem was discovered by the French mathematician De Moivre. In his excellent paper published in 1733, he used normal distribution to estimate the distribution of times when a large number of coins were thrown. This transcendental achievement is almost forgotten by history. Fortunately, Laplace, a famous French mathematician, saved this obscure theory in his famous book Analytic Probability published in 18 12.