学习《概率论与数理统计》应该注意的若干问题（4）——正态分布在抽样分析中的地位

正态分布是随机变量分布中基础而且核心的分布。中心极限定理支持这样的结果：通过统计的手段,对任一个随机变量的分析和研究,可以借助于正态分布进行。在数理统计的抽样分析中,由（标准）正态分布的统计量的适当组合,产生数理统计中的其他三大基础分布。     

混合序列的完全收敛性

讨论了ρ混合序列的完全收敛性,推广了已有文献中关于ρ混合序列的完全收敛性的结果,并把此结论推广到不同分布的情形.     

Formulating and Using Probability Density Functions with Familiar Geometric Shapes

This note shows how some density functions for continuous probability distributions can be constructed in a transparent manner to help students appreciate their development.     

非线性带涂层圆柱形复合介质的电势分布

利用摄动方法,研究了在外加交流电场E=E1sinωt＋E2sin3ωt＋E5sin5ωt的作用下,非线性带涂层圆柱形复合介质的电势分布,这种介质的电流密度J和电场强度E之间满足的关系为Jα=σαE＋χα｜E｜2E。     

关于多项式实零点的某些公开问题

本文回答Shapiro了提出的关于Narayana矩阵和Fibonacci矩阵的行的极限分布的公开问题,并给出了简单证明.     

论话语权

本文认为建立平等、友善、互助、和谐的人际关系是话语权得以公平分布、顺利实施的基本条件。文章分析了话语权分布的倒金字塔型、伞字型、口字型和逆向对等型,探讨了滥用、占用、弃用和慎用话语权等现象,讨论了正导、误导、强导和祈导话语权等问题,从构建和谐社会与和谐语言的角度论述了话语权的重要性。     

破产分布及其方程

In this paper, the ruin distributions were analyzed, Including the distribution of surplus immediately before ruin, the distribution of claim at the time of ruin, the distribution of deficit, and the distribution of surplus at the beginning of the claim period before ruin. Several Integral equations for the ruin distributions were derived and some solutions under special conditions were obtained.     

Mean and Variance through Factorial Moments

This article shows how the use of factorial moments provides a simple, consistent yet elegant approach to finding the mean and variance of standard discrete probability distributions.     

离散型随机变量常见分布列中的极值

讨论了分布函数p(ξ=k)=p(k)的极值问题,并给出了一种求离散型分布列函数极值的一种简便算法--比值法.     

A distributional analysis of the effect of physical exercise on a choice reaction time task

Abstract

The aim of this study was to examine the facilitating effects of physical exercise on the reaction process. Eleven participants with specific expertise in decision-making sports performed a choice reaction time task during moderate sub-maximal exercise (90% of their ventilatory threshold power). Participants were tested at rest and while cycling. During exercise, the participants were faster, without being more variable. We suggest that the effect of exercise on cognitive performance was due to a major generalized improvement of the whole distribution of response time and, although the benefit effect was small, it was consistent throughout the entire range of reaction times.