Abstract: or uncorrelated random vectors have many good properties. It is not enough to determine the uncorrelativity or independency just by virtue of its definition and intuition. First, it summarized the methods of determining independence or uncorrelated random vectors. It is important to avoid judging errors. Then, some examples were given, based on these methods. Finally, the expansion of these methods was proposed.

Key words: random vectors; normal distribution; un-correlativity; independency