积分变换在连续型独立随机变量线性组合分布问题中的应用  

The application of integral transformation in the distribution problem of linear combination of continuous independent random variables

作　　者：孙立伟[1] 张志旭[1] SUN Li-wei;ZHANG Zhi-xu(School of Science,Jiamusi University,Jiamusi 154007,China)

机构地区：[1]佳木斯大学理学院,黑龙江佳木斯154007

出　　处：《高师理科学刊》2018年第10期16-18,共3页Journal of Science of Teachers＇College and University

基　　金：黑龙江省科研业务费项目(2017-KYYWF-0569)

摘　　要：多个相互独立随机变量和的概率密度需要进行若干次卷积运算,是概率论课程中计算较繁琐的部分.利用Fourier变换和Laplace变换等证明了有限多个相互独立随机变量和的概率密度以及任意线性组合的概率密度问题的相关结论.The probability density of the sum of multiple mutually independent random variables requires several convolution operations,which is a more cumbersome part of the calculation in the probability theory course.Use Fourier transform and Laplace transform and other related knowledge to prove relevant conclusions about the probability density of the sum of a finite number of mutually independent random variables and probability density problems of arbitrary linear combinations.

关 键 词：FOURIER变换 LAPLACE变换 卷积定理 正态分布 G分布可加性 

分 类 号：O177[理学—数学]