1、 I 摘摘 要要 随着经济的不断发展，随机变量和的分布在金融、保险和精算等领域中的应 用也越来越广泛，因此对于随机变量和的理论研究也非常的重要，本文总结了求 随机变量和的分布的方法，并给出了常用独立同分布随机变量和的分布。 本文首先介绍了随机变量和的分布的研究背景和研究意义。其次，介绍了常 用的随机变量及其相关性质。再次，总结了一些特殊类型的独立同分布随机变量 和的精确分布。对于某些随机变量和的精确分布不存在的随机变量，本文给出了 两种处理方法。当变量的个数很多时，可以利用独立同分布的中心极限定理来给 出独立同分布随机变量和的近似分布，即正态分布；当变量的个数不是很多时， 可以利用 Monte
2、 Carlo 方法， 并结合科学计算软件 MATLAB 和统计软件 SPSS 来模 拟随机变量和的分布。最后给出了随机变量和的分布的几个简单应用。 关键字：二项分布，正态分布，Monte Carlo 方法，随机数 II Abstract With the constant development of economy, the distribution of the sum of random variables is applied to many fields, such as financial, insurance, actuary and so on. So the study of
3、 the theory for the sum of the random variables is also very important. This paper summarizes the methods of solving the distribution of the sum of random variables and gives the distribution of the sum of the independent and identically distributed random variables which is commonly used. This pape
4、r firstly introduces the research background and research significance of the distribution of the sum of random variables. Secondly, this paper introduces the commonly used random variables and their associated properties. Then this paper summarizes accurate distribution of some special types of the
5、 distribution of the sum of random variables which is independent and identically distributed. For some random variables which the precise distribution of the sum of random variables does not exist, this paper gives two kinds of processing method. When there are a lot of variables, the approximate d
6、istribution of the distribution of the sum of random variables which is independent and identically distributed can be given by using central limit theorem of independent and identically distributed, namely the normal distribution. When there are few variables, Monte Carlo method can be used, and combined with scientific computing software MATLAB and statistical software SPSS to simulate the distribution of the sum of random variables. Finally, this paper gives a few simple applications about II
