正态分布概率密度函数与数字特征的关联性研究OA

This paper investigates the identification of the probability density function of nor-mal distribution and the correlation of its numerical characteristics.Since the original func-tion of the normal distribution probability density function is not an elementary function,its statistical properties must be determined through improper integrals,which limits its practi-cal applications.Moreover,the determination of two-dimensional normal distribution is particularly complex.This study approaches from double integrals and,combined with the properties of positive definite matrices,derives the key criteria for determining one-dimen-sional and two-dimensional normal distribution probability density functions and proposes a rapid determination method based on function parameters.At the same time,it delves into the quantitative relationship between core digital characteristics of the normal distribution and the coefficients of the probability density function parameters and the validity of the con-clusions is verified through application examples.The research results provide a theoretical basis for the rapid identification of normal distributions and can be directly applied in the field of statistics to improve sampling distribution efficiency and lay a foundation for the con-struction of parameter conversion models.