毕业论文大数定律在经济学中的应用

学校代码：10206

学生学号：*********

白城师范学院

毕业论文（设计）

大数定律在经济学中的应用Law of large numbers in economics

学生姓名：***

指导教师：邬伟三讲师

学科专业：数学与应用数学

所在单位：数学系

2011年6月

摘要

概率论历史上第一个极限定理属于伯努利，后人称之为“大数定律”。概率论中讨论随机变量序列的算术平均值向常数收敛的定律。概率论与数理统计学的基本定律之一。

有些随机事件无规律可循，但不少却是有规律的，这些“有规律的随机事件”中在大量重复出现的条件下，往往呈现几乎必然的统计特性，这个规律就是大数定律。

通俗地说，这个定理就是，在试验不变的条件下，重复试验多次，随机事件的频率近似于它的概率。这种情况下，偶然中包含着必然。必然的规律与特性在大量的样本中得以体现。

大数定律是概率论中的重要内容,它以严格的数学形式表达了随机现象最根本的性质——平均结果的稳定性,它是随机现象统计规律性的具体表现,在数学应用及经济生活中有着较为重要的作用,较多文献给出了不同条件下存在的大数定律,并利用大数定律和中心极限定理得到较多模型的收敛性,但对于它们的适用范围及在实际生活中的应用涉及较少。本文就大数定律做了具体的分析,介绍了几种较为常见的大数定律,并结合它们存在的条件的不同,分析了它们各种适用的数学模型的特征,列举了它们在经济生活领域的应用,将理论具体化, ,以使得枯燥的数学理论与实际想结合,使大家对大数定律在实际生活中的应用价值有了更深的认识。

关键词：大数定律特征函数保险银行贷款

Abstract

A history of probability limit theorem is Bernoulli, later known as the "law of large numbers." Probability random variables discussed in the arithmetic mean law of convergence to the constant. Probability theory and mathematical statistics one of the basic laws.

Some random events without a pattern, but many are regular, these "regular random incident," a large number of recurring conditions, often showing statistics of almost inevitable, this rule is the law of large numbers.

In layman's terms, this theorem is that under the same conditions in the test, repeat testing several times, the frequency of random events similar to it probability. In this case, includes the inevitable accident. The regularity and characteristics of the inevitable large number of samples to be reflected.

Law of large numbers is an important part of probability theory, its rigorous mathematical form, the most fundamental expression of the random nature of the phenomenon - an average of the stability of results, it is the statistical regularity of random phenomena of specific performance, application and economic life in mathematics has a more important role, more literature exists under different conditions are given law of large numbers, and using law of large numbers and central limit theorem, the convergence of many models, but their scope of application and in real life The applications involve small. This paper made a law of large numbers of specific analysis, introduces some of the more common law of large numbers, combined with their existing conditions, the analysis of their mathematical model for a variety of features, listed them in the field of economic life the application of the theory specific, in order to make the boring mathematical theory and practice was integrated so that people in the law of large numbers of applications in real life have a deeper understanding of the value.

Keywords：Law of Large Numbers Characteristic function Insurance Bank loans