Based on studying and analyzing ample first hand information during the historic period of Shan-Gan-Ning Boarder Area,the paper finds it quite necessary to explore Xie\'s thoughts on ruling by law,particularly his judiciary thoughts,in which the semi-independence of justice and the balance between experts\' justice and people\' justice had most outstanding features.

This paper proves at first that any two non correlative random variables are still non correlative through linear transformation and the independent random variables of normal distribution are still independent each other through this kind of transformation.