二维正态随机变量的线性组合的独立性  

On the Independence of Linear Combinations of Bivariate Normal Random Variables

作　　者：邹云蕾 ZOU Yun-lei(School of Mathematical Sciences,Yangzhou University,Yangzhou,Jiangsu 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《教育教学论坛》2020年第15期279-280,共2页Education And Teaching Forum

摘　　要：正态分布是实际生活中应用最广泛的一种概率分布。文章讨论了服从二维正态分布的随机变量(X,Y)的线性组合U=a X+b Y和V=c X+d Y的独立性问题,并基于变换矩阵给出了(U,V)的分布与(X,Y)的分布之间的联系,得到了U和V独立的充要条件,同时,分析了U和V独立的条件下(U,V)的分布。Normal distribution is a kind of the most widely used probability distribution in daily life. In this paper,the independence problem of U=a X+b Yand V=c X+d Y,where(X,Y)are bivariate normal random variables,is discussed.Based on the transformation matrix,the distributing relationship of(U,V) and(X,Y) is given,and some necessary and sufficient conditions for independence of Uand V are obtained. Besides,under the condition that U and V are independent,the distribution of(U,V) is analyzed.

关 键 词：二维正态分布 线性组合 独立性 变换矩阵 

分 类 号：G642.4[文化科学—高等教育学]