判定二维随机变量服从正态分布的一个充分条件

A Sufficient Condition for Determining the Normal Distribution of Two-dimensional Random Variables

探讨了二维随机变量服从正态分布的一个充分条件.在两个不相关的随机变量的任意正整数线性组合都是正态随机变量的条件下,利用矩生成函数证明了它们分别服从正态分布,且联合分布也是二维正态分布.

A sufficient condition for normal distribution of two-dimensional random variables is discussed.Under the condition that any linear combination of any two positive integers of two unrelated random variables is normal random variable,it is proved by the monent generating function that they are subject to normal distribution respectively,and the joint distribution is also a binary normal distribution.