基于MATLAB的De Moivre-Laplace中心极限定理的随机模拟

Random Simulation of De Moivre-Laplace Central Limit Theorem

针对De Moivre-Laplace中心极限定理,首先利用特征函数和独立同分布下的中心极限定理得到理论上证明,然后利用MATLAB软件随机模拟分析二项分布与正态分布之间的关系,并对图像进行误差分析,最后证明数值结果与实验结果的一致性。通过这两种不同角度的论证,给出De MoivreLaplace中心极限定理直观的解释和说明,这种将数学实验与数学原理结合的方法,不仅使数学原理化抽象为具体,便于理解和实践,而且扩展了数学原理和计算机软件的应用。

Based on De Moivre-Laplace Central Limit Theorem,first,this paper gives a theoretical proof on the theorem by characteristic function and Lindeberg- Levy Theorem. Second,this paper explains and simulates the relationship between normal distribution and binomial distribution by using MATLAB software,and then analyzes the error for the image that is produced by the MATLAB software. Last,prove that the numerical result and the analysis result are consistent. By these two different angles of argument,this paper gives the intuitive explanation and illustration of Moivre-Laplace De central limit theorem. This method combined mathematical experiment and mathematical principles,not only makes mathematical principles specific,easy to understand and practice,but also extends the application of the mathematical principles and computer software.