| 随机变量内积空间 |
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| 引用本文： | 侯文超.随机变量内积空间[J].北京工商大学学报(自然科学版),2007,25(6):82-84. |
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| 作者姓名： | 侯文超 |
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| 作者单位： | 北京工商大学,北京,100037 |
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| 摘 要： | 对概率空间{Ω,A,P}上的具有二阶矩的随机变量的全体作了等价分类,构造了内积空间,把内积、范数、夹角等概念与协方差、标准差、相关系数联系起来,建立了正交分解定理,给出相关系数概率意义的更清楚的解释.
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| 关 键 词： | 随机变量 内积 正交分解定理 |
| 文章编号： | 1671-1513（2007）06-0082-03 |
| 收稿时间： | 2007-04-22 |
| 修稿时间： | 2007年4月22日 |
INNER PRODUCT SPACE OF RANDOM VARIABLES |
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| HOU Wen-chao.INNER PRODUCT SPACE OF RANDOM VARIABLES[J].Journal of Beijing Technology and Business University:Natural Science Edition,2007,25(6):82-84. |
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| Authors: | HOU Wen-chao |
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| Abstract: | This paper sorts all random variables with second moment on the probability space according to equivalent relation, and constructs the inner product space. The inner product, the norm and the angle of intersection on the inner product space link up accordingly with the covariance, the standard deviation and the correlation efficient on the theory of probability. The correlation coefficient is given a clear explanation by established orthogonal decomposition theorem. |
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| Keywords: | random variable inner product orthogonal decomposition theorem |
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