| 向量理论在概率论中的应用 |
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| 引用本文： | 刘龙飞,张同琦,李凤.向量理论在概率论中的应用[J].渭南师范学院学报,2010,25(5):10-12. |
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| 作者姓名： | 刘龙飞 张同琦 李凤 |
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| 作者单位： | 渭南师范学院,陕西,渭南,714000 |
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| 摘 要： | 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.
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| 关 键 词： | 随机变量 零变量 向量空间 欧氏空间 |
Application of Vector Space in Probability |
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| LIU Long-fei,ZHANG Tong-qi,LI Feng.Application of Vector Space in Probability[J].Journal of Weinan Teachers College,2010,25(5):10-12. |
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| Authors: | LIU Long-fei ZHANG Tong-qi LI Feng |
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| Institution: | (Weinan Teachers University,Weinan 714000,China) |
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| Abstract: | 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. |
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| Keywords: | random variable null variable vector space Euclidean Space |
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