The Gaussian distribution: Derivation method and its applications in selected examples

Abstract

Gaussian distribution is the most important and common form of distribution in statistical theory, and its density function has more complicated forms. When Gauss dealt with the problem of measurement error, he derived the form of normal distribution from another angle, and proposed the least squares theory based on the normal distribution of error. This helps solve the problem of the probability density distribution of the error, enabling people to make a better statistical measure of the effect of the size of the error. In short, Gaussian distribution is not only a powerful mathematical tool, but also a connection between theory and practical applications. It is also a bridge between theory and practical application. In practice, the Gaussian distribution has a wide range of applications, in the natural sciences, engineering and social sciences and other fields, the Gaussian distribution is used to describe the continuity of random variables, such as measurement error, temperature change, population intelligence level. In this paper, the author briefly deduces the Gaussian distribution derivation process, from the overall and the measurement error of the simple random samples to cut in, to admit that x is already the estimates that should be taken. Hopefully, it will be helpful to scholars who are interested in this area.