基于使用正态分布描述"醉汉随机游走"问题步长的实验教学案例分析
首发时间:2020-07-02
摘要:为了提高《概率论与数理统计》这一课程的教学质量,推动该课程的教学改革,培养学生的数据分析能力,本文针对"醉汉随机游走"实验设计了一个全新的教学案例,运用正态分布描述醉汉随机游走问题中步长的概率分布,探究了醉汉步数与当步长服从正态分布时其参数对醉汉游走的平均距离和方差的影响。本文作者根据问题描述进行建模后,再通过python软件模拟仿真,得出了步数,步长的期望和标准差与平均距离、方差的关系。使用该教学案例教学不仅可以深化学生对该课程知识的理解,而且可以加强学生对计算机仿真的实际操作能力,提高学生学习效率,使学生的个人能力更加符合社会的需要。
关键词: 统计实验教学 概率论与数理统计 正态分布 python仿真
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Based on the normal distribution to describe the drunkard random walk problem step length experimental teaching case analysis
Abstract:In order to improve the teaching quality of probability theory and mathematical statistics, promote the teaching reform of the course, and cultivate the students\' data analysis ability, this paper designs a new teaching case for the "drunk random walk" experiment. Normal distribution is used to describe the probability distribution of the step size in the drunk random walk problem. The influence of drunk step size and its parameters when the step size obeys the normal distribution and on the average distance and variance of drunk walk is explored. Modeling is carried out according to the problem description. Through python simulation, the relationship between the step size, expectation and standard deviation of the step size and the average distance and variance is obtained. Using this teaching case teaching can not only deepen students\' understanding of the course knowledge, but also strengthen students\' practical operation ability of computer simulation, improve students\' learning efficiency, and make students\' personal ability more in line with the needs of society.
Keywords: Statistical experiment Simulationteaching Probability theory and mathematical statistics Normal distribution
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基于使用正态分布描述"醉汉随机游走"问题步长的实验教学案例分析
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