Pedagogical Simulation of Sampling Distributions and the Central Limit Theorem

Students often find the fact that a sample statistic is a random variable very hard to grasp. Even more mysterious is why a sample mean should become ever more Normal as the sample size increases. This simulation tool is meant to illustrate the process, thereby giving students some intuitive grasp of the relationship between a parent population and the distribution of a sample mean.     

Optimal Keno Strategies and the Central Limit Theorem

For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is reinforced.     

中心极限定理在实际中的应用

中心极限定理是阐明有些即使原来并不服从正态分布的一些独立的随机变量,它们的总和渐近地服从正态分布.对概率论中的三个重要中心极限定理进行了论述,并总结了它们各自在实际中的应用.     

中心极限定理在质量控制中的应用

介绍De Movire—Laplace定理,给出该定理在质量控制中的广泛应用。     

中心极限定理在抽样推断中的应用

讨论中心极限定理在抽样推断中的若干应用。     

The Power of Doing: A Learning Exercise that Brings the Central Limit Theorem to Life

This article demonstrates an active learning technique for teaching the Central Limit Theorem (CLT) in an introductory undergraduate business statistics class. Groups of students carry out one of two experiments in the lab, tossing a die in sets of 5 rolls or tossing a die in sets of 10 rolls. They are asked to calculate the sample average of each experiment. An easy‐to‐use Excel template is designed to calculate the averages from the students' dice rolls. Empirical histograms are generated dynamically for both sample sizes of 5 and 10 rolls, visually demonstrating the convergence toward a bell‐shaped distribution for the sample means. Our classroom experiences with the learning approach show that most students view it as fun and valuable to their learning of the concepts underlying the CLT.     

Illustrating Dependence between Random Variables Using Slot Machines

This article illustrates the concept of statistical independence using the example of slot machines that may be played on multiple lines.     

极限定义验证极限

极限概念是数学分析的最基本概念,用“ε-N”方法验证数列的极限、用“ε-δ”方法验证函数的极限是加深理解极限概念的重要途径,又是学生学习的难点,为突破难点,文章提供了一些证题思路和方法 。     

A Story‐based Simulation for Teaching Sampling Distributions

Statistical inference relies heavily on the concept of sampling distributions. However, sampling distributions are difficult to teach. We present a series of short animations that are story‐based, with associated assessments. We hope that our contribution can be useful as a tool to teach sampling distributions in the introductory statistics classroom.     

测度的摄动法与幂级数分布的一个强大数定理

在文献[1]的基础上，以幂级数分布为例，给出了证明大数定量一个新方法－测度的摄动法。     

Riemann积分的一个极限定理

研究了Riemann积分意义下积分与函数列极限的交换问题．利用Riemann可积函数控制及函数列的亚一致收敛性．得到了Riemann积分的一个极限定理．     

大数定律及中心极限定理在保险中的应用

文中研究了大数定律及中心极限定理的含义及关系,阐述了它们在制定保费及自留额、拟定保险单位数及减少保险个人平均危险值等方面的应用．     

Illustrating the Dangers of Hunting the Process Mean

This article describes two simple ways to illustrate the important concept in statistical process control known as “hunting”. The two simulations use dice and Minitab respectively.     

Simulation in the Simple Linear Regression Model

This article presents an activity which simulates the linear regression model in order to verify the probabilistic behaviour of the resulting least‐squares statistics in practice.     

Hazard函数估计误差的极限定理

令H_n(x)是基于来自密度函数f(x)的容量为n的一个随机样本的hazard函数H(x)=f~(x)/[1-integral from x=∞ to x(f(t)dt)]的一个核形估计.对于非参数hazard估计的积分均方误差integral ((H_n(x)-H(x))~2ω(x)f(x)dx)中心极限定理成立的一个充分条件被给出,这里ω(x)是一个权函数.     

What Divisor for the Sample Variance?

Simulation is used to show why the divisor in the sample variance is n, - 1. Choice of the divisor for the sample standard deviation is also discussed.