向量理论在概率论中的应用

Application of Vector Space in Probability

通过在概率论中引入"零变量"概念,将向量空间理论应用于概率论的研究中,得到了同一样本空间Ω上的全体随机变量所成的集合是一向量空间的结论,并且证明了两个随机变量ξ,η的协方差即是向量ξ,η的内积<ξ,η>,继而得出同一样本空间Ω上的全体随机变量所成集合为一欧氏空间,从代数学的角度给予了概率论中的若干概念全新的解释.

By introducing the null variable in probability,we apply vector space theory in probability and obtain that set made of random variable of same sample space constructs a vector space,and prove that covariance COV of two sample variable is inner product of vector.Further,we conclude that set made of total random variable of same sample space is a Euclidean Space.Thus we can explain some definitions of probability at the point of algebra.