中文摘要：

正态总体下样本均值与样本方差的独立性是数理统计学教学中的重要结论。从构造特殊正交矩阵,利用随机向量的线性变换与随机向量的二次型相互独立的条件,特征函数和矩母函数这四个方面,证明了正态总体下样本均值与样本方差的独立性。

英文摘要：

The independence of sample mean and sample variance under the normal population is a very important theorem in the teaching of mathematical statistics. In this paper,we give the proofs of the conclusion from four aspects,including the construction of a special matrix,condition of the independence of the quadratic form and the linear transform of a normal random vector,characteristic function and moment generating function.