大数定律与中心极限定理的关系及其应用.pdfVIP

论文题目：大数定律与中心极限定理的关系及其应用 摘 要：本文通过对概率论的经典定理——大数定律与中心极限定理在独立同分布和不 同分布两种情况下的结论作了比较系统的阐述,揭示了随机现象最根本的性质——平均 结果的稳定性.经过对中心极限定理的讨论,给出了独立随机变量之和的分布可以用正 态分布来表示理论依据.关于大数定律方面,较全面地分析和叙述了几种最常用的大数 定律.同样中心极限定理的内容也从独立同分布与独立不同分布两个角度来进行讨论 ; 另外,叙述了各种大数定律以及中心极限定理各自之间 ,大数定律与中心极限定理之间 的关系.同时通过举出很多相关的反例说明二者的关系.最后给出了一些简便的大数定 律与中心极限定理在数理统计、误差、彩票学、近似计算、保险业及数学分析等几个方 面的应用,来进一步地阐明了大数定律与中心极限定理在各分支学科中的重要作用和应 用价值. 关键词：随机变量序列；大数定律；中心极限定理；应用 Title ：Law of large numbers and the relationship between the central limit theorem and its application Abstract: Based on the probability of a classic theorem : the law of large numbers central limit theorem in the independent distribution ; with the different distribution of both cases, it made more systematic exposition, and revealed the phenomenon of the random nature of the most fundamental an average of the results of the Stability . Trough the central limit theorem discussion it will give out the random variables and the distribution of the normal distribution .About the law of large numbers, there are more comprehensive analysis and described several of the most commonly used on it. The content of the same central limit theorem also discussed the independent distribution and independent distribution of the two different perspectives. Also, it will discussed the relationship between the variety of na ative and the law of large numbers between their respective central limit theorem, and that of the law of large numbers and the central limit theorem. At the same time, it demonstrated the relationship between the two aspects through lots of anti-related examples. Finally ,it gave out several aspects of application of a number of simple law of large numbers and the central limit theorem in mathematical statistics, e or, lottery school, the approximate calculation, and the insurance industry a