Viewing the historical origin of normal distribution from the brief history of mathematical statistics

Title:Viewing the historical origin of normal distribution from the brief history of mathematical statistics...

Complete History

This section will combine with the book A Brief History of Mathematical Statistics, from the early development of probability theory, Dimoffer’s binomial probability approximation to Bayesian method, least squares method, error and normal distribution, etc., 

there are some details. , Which focuses on the historical origin of the normal distribution.

As seen in the first three sections above, in the textbooks of probability theory and mathematical statistics, the normal distribution is introduced first, and then its probability density distribution function is given, but it has never been explained by what principle this distribution function is derived. In this way, many people, including you and me, may never understand how mathematicians found this probability distribution curve, and how they discovered that random errors obey this wonderful distribution. We use the normal distribution a lot in practice, but we don't know much about the ins and outs of this distribution.

     The next fourth section of this article will combine Academician Chen Xiru's "A Brief History of Mathematical Statistics" and "The Past and Present of Normal Distribution" to uncover the mystery of normal distribution.

4.1. Definition of normal distribution The related definition of normal distribution has been given above, let's review it first. As shown in the following two figures (source: Big Mouth Talking about Data Mining):

I believe that after the bombardment of many complicated formulas above, readers may be a little impatient. Let's talk about something interesting next: history. Next, let's combine the book A Brief History of Mathematical Statistics, the past and present series of normal distribution, to discuss the historical origin of normal distribution from ancient times to the present.

4.2. Early Probability Theory: From Germination to Speculation 4.2.1. Three Theorems on Expectation of Huixin (1) The Calculation of Huixin's Theory of Gambling
    The so-called probability refers to a quantitative indicator of the probability that an event occurs and a situation occurs. It is between 0 and 1. This concept was originally formed in the 16th century. It may surprise you. There is no absolute in the early days. Many discussions in probability theory are inextricably linked to gambling activities that seem to be illegal and criminal today, such as rolling dice. It can be said that these gambling activities have promoted the early development of probability theory.
    History is complicated. Let's start with Huygens' Law of Opportunity. This person taught Leibniz, one of the founders of calculus, to study mathematics. He also interacted with Newton and others. He was unmarried all his life. Like many famous figures in history, the reason why they are remembered by future generations is because of their outstanding contribution in a certain field. This contribution may be a certain theorem or formula. In other words, it is the present day. The representative work that people say has the same meaning.

     What Hui Gengxin is familiar to contemporary people should be that he put forward the formula of the pendulum swing period in the history of physics in the papers "Pendulum Clock or the Geometric Proof of the Movement of the Pendulum Used on Clocks" and "Pendulum Clock"

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