关于正态随机变量线性组合分布的反例构造

任意n个正态随机变量之和不一定是正态随机变量,反例较难构造和证明,文献1]给出了Rosenberg例。本文用其他方法构造了两个及任意n个非独立的正态随机变量线性组合不是正态随机变量例子,且证明方法也较简便。同时,将Rosenberg例进行了推广。通过反例的构造与证明,对正态随机变量线性组合分布的理解与应用有一定意义。

An Opposite Example about the Distribution of Linear Combination of Abnormal Random Variables

The sum of abnormal random variables of random n is not necessarily abnormal random variables. An opposite example is difficult to find and prove.The document l]gives the Rosenberg example.By using other methods,this article gives an example to show that non - independent linear combination of abnormal random variables of two and random n is not necessarily abonrmal random variables. The proof method is simple.This example is significant to the understanding and application of the distribution of linear combination of abnormal random variables.