关于正态随机向量的独立性与相关性的一个问题

A Problem on Independence and Correlativity of Normal Random Vectors

给出两个正态随机向量不独立且不相关的例子；证明了取自两个正态总体的两个简单随机子样Ｘ与Ｙ当（Ｘ，Ｙ）τ为正态随机向量时（特别，当两子样独立时）两子样方差仍相互独立．

An example showing that two uncorrelated normal random vectors are not independent is given. It has been proved that for two simple samples from two normal populations X and Y , if ( X,Y )' is normal (specially, if X,Y are independent) then two sample variances are independent.