应用变量变换法讨论2维正态分布的性质

Using Variable Transformation to Discuss the Properties of Bivariate Normal Distribution

运用通常方法讨论2维正态分布的性质时,计算较为繁琐。以变量变换法为工具,给出一个独立性定理,以变量变换法和该独立性定理为基础,讨论2维正态分布的边际分布、协方差、独立性,可以看到该方法显著地减少了计算量。

The amount of calculation is too large when we discuss properties of the bivariate normal distribution using the usual method.At first,this paper proves an independence theorem by variable transformation method,then studies marginal distributions,covariance and independence of bivariate normal distribution based on variable transformation method and the independence theorem.At last,we find that it can greatly reduce the amount of calculation.