一维正态分布的随机变量独立与不相关研究

The Study on the Independence and Uncorrelated of One-Dimensional Normal Random Variables

两个一维正态分布的随机变量的独立与不相关的问题,是概率论与数理统计中一个热点问题.若两个随机变量X与Y均服从一维正态分布,其联合分布不一定服从二维正态分布.由于随机变量X与Y相互独立,一定有X与Y不相关,反之如果随机变量X与Y不相关,不能够得到X与Y相互独立.

The independence and uncorrelated problems of two random variables with one - dimension normal distribution are hot problems in probability theory and mathematical statistics. If two random variables X and Y obey one - dimensional normal distribution, their joint distribution does not always obey two - dimensional normal distribution. Since the random variables X and Y are independent of each other, there must be uncorrelated between X and Y. Conversely, if the random variables X and Y are uncorrelated , then we can not get X and Y independent of each other.