随机变量在线性变换下的不相关性和独立性

Non-correlativity and independency of random variable in linear transformation

本文先证明了两两不相关的随机变量在一类线性变换下仍然是两两不相关的 .从而得出相互独立的服从正态分布的随机变量在此类变换下仍然是相互独立的 .然后进一步讨论有同方差的两两不相关的随机变量在准正交变换下的两两不相关性 ,得出有同方差的相互独立的正态分布的随机变量 ,在准正交变换下的一系列结果 .最后将关于n维正态分布性质的引理[5] 进一步完善、推广 。

This paper proves at first that any two non correlative random variables are still non correlative through linear transformation and the independent random variables of normal distribution are still independent each other through this kind of transformation. And then the non correlativity is discussed for non correlative random variable with the same square differences through“quasi orthogonal transformation”.So that we have several conclusions about independent normal distributed random variables with the same square difference through“quasi-orthogonal transformation”.Finally by making the preparation theorem of the property of n dimension normal distribution [5] to be more perfect,a specific method of finding transform matrix is shown.