R语言在概率统计课堂教学中的应用--中心极限定理随机模拟

Statistical Classroom Teaching Based on R Software—Stochastic Simulation of the Central Limit Theorem

中心极限定理是概率论与数理统计中非常重要的知识点,是数理统计的理论基石,借助R软件设计相关辅助教学案例进行数据模拟实验;首先进行两种方式的数据模拟:一是进行随机采样后加和生成新的数据列;二是通过卷积推导出和变量的密度函数;然后分别绘制密度函数线,查看分布情况;最后通过高尔顿钉板实验的教学案例,用可视化的实验结果形象解释该理论。

The central limit theorem is a very important knowledge point in probability theory and mathematical statistics,and it is the theoretical cornerstone of mathematical statistics.This paper uses R software design related auxiliary teaching cases to carry out data simulation experiments.Firstly,two ways of data simulation are performed:one is to add and generate new data columns after random sampling,the other is to derive the density function of the variables through convolution.And then,draw the density function line separately to view the distribution.Finally,through the teaching case of Galton nail plate experiment,the theory is vividly explained with visual experimental results,which not only deepens the students’interpretation of the knowledge point,but also improves the students’practical ability.