随机变量的可逆线性变换的分布
首发时间:2013-09-04
摘要:设连续型的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,设变换的矩阵为A,本文证明了,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。证明的方法是,首先证明X做一次初等变换时定理成立,然后再利用归纳法可证。
关键词: 概率论 随机变量的函数的分布 线性变换
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The distribution of revertible linear transformation of random variables
Abstract:Let n-dimensional random variables X through reversible linear transfom into n-dimensional variables Y , and the transform matrix is A. This paper has proved that the probability density of Y can be got by doing reverse transformation from arguments of probability density of X then being divided by the determinant of A. The method of proving is that first prove the thoerem is true when doing one elementary transformation, then use induction.
Keywords: probability theory distribution of function of random variable linear transformation
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