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随机变量的可逆线性变换分布

发表时间:2014-01-15  浏览量:1734  下载量:517
全部作者: 陈必红
作者单位: 深圳大学数学与计算科学学院
摘 要: 设连续型n维随机变量X经过可逆的线性变换变为n维随机变量Y,设变换矩阵为A,首先证明X做一次初等变换时定理成立,然后再利用归纳法证明Y的概率密度函数是X的概率密度函数中自变量做逆变换,且前面除以A的行列式的绝对值。
关 键 词: 概率论;随机变量的函数分布;线性变换;局部反函数;条件分析法
Title: Distribution of revertible linear transformation of random variables
Author: CHEN Bihong
Organization: College of Mathematics and Computational Science, Shenzhen University
Abstract: Let n-dimensional random variables X through reversible linear transfom get n-dimensional variables Y, and the transform matrix be A. The proving method is that it firstly proves the thoerem is true when X doing one elementary transformation, then uses induction to prove it.This paper has proved that the probability density of Y can be gotten by doing reverse transformation from arguments of probability density of X, and then is divided by the determinant of A.
Key words: probability theory; distribution of function of random variable; linear transformation; local inverse function; conditional analysis
发表期数: 2014年1月第1期
引用格式: 陈必红. 随机变量的可逆线性变换分布[J]. 中国科技论文在线精品论文,2014,7(1):8-15.
 
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