2014某人论文范本.doc

2014 某人论文范本安徽大学本科毕业论文(设计) 题目: 随机变量列的各种收敛性及其性质学生姓名: 仝猛学号:院(系): 数学科学学院专业: 统计学入学时间:二○○四年九月导师姓名: 汪世界职称/ 学位: 讲师导师所在单位: 安徽大学数学科学学院-1- 随机变量列的各种收敛性及其性质摘要概率论是研究大量随机现象中的数量规律的数学分支, 研究随机变量是它的重要任务, 而概率论中所研究的也大都能用随机变量来描述的随机现象。随机变量是定义在样本空间上具有某种可测性的实值函数。用随机变量描述随机现象是近代概率论中最重要的方法。随机变量具有各种收敛性及其它一些重要的性质。概率论的极限理论就是一些关于随机变量及其分布的极限性质和收敛性的论断,它们在理论和应用中都很重要. 随机变量有许多种收敛性, 这里将介绍四种收敛性: 依概率收敛, 依概率 1 收敛, 平均收敛, 依分布收敛, 及其四种收敛性的关系。在依分布收敛中, 我们将主要应用两类极限定理, 一类是“大数定理”, 一类是“中心极限定理”. 大数定理和中心极限定理在实际中有着重要的应用。关键词:随机变量收敛性;依概率收敛;依概率 1 收敛;平均收敛; 依分布收敛;关系;大数定理;中心极限定理. -2- Various Kind of Convergence and Property of Random Variables Abstract Probability theory which studies quantitative law of massive random phenomenon isa branch of mathematics and. Its important task is to study the random variables. The random phenomenon can be mostly described by random variables in probability. The random variable defined in the sample space is some kind of measurable real-valued function. It is the most important method to describe the random phenomenon by the random variable in the modern theory of probability. The consequence of random variables has various kinds of convergence and property. The limit theory of probability theory is some limit property and convergence judgment about the random variables and their distributions which are very important both in theory and in application. The random variable has many kind of convergence, and we will introduce four kinds of them: convergence in probability, convergence almost everywhere, convergence in moment, convergence in distribution, and then their relations are also given. In accordance with the convergence in distribution, we will mainly use two types of limit theorem, one of which is "the law of large number ", and the other is "central limit theorem ”. Both have important applications in practice. Keywords: the convergence of random variable; according to probability convergence; according to probability 1 convergence; mean convergence; according to convergence in dist