| 一个方差公式的多种证明 |
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| 引用本文： | 王敏慧,刘国庆,张银龙. 一个方差公式的多种证明[J]. 大学数学, 2012, 28(1): 165-167. DOI: 10.3969/j.issn.1672-1454.2012.01.035 |
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| 作者姓名： | 王敏慧 刘国庆 张银龙 |
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| 作者单位： | 1.哈尔滨师范大学,黑龙江哈尔滨,150025;2.哈尔滨工业大学数学系,黑龙江哈尔滨,150006;3.装甲兵技术学院数学教研室,吉林长春,130117 |
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| 摘 要： | 运用方差性质,协方差定义,函数凸性等方法,给出一个方差公式Var max（a,X）≤Var X的多种证明.
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| 关 键 词： | 方差 协方差 独立同分布 凸函数 |
A Various Proofs on a Variance Formula |
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| WANG Min-hui,LIU Guo-qing,ZHANG Yin-long. A Various Proofs on a Variance Formula[J]. College Mathematics, 2012, 28(1): 165-167. DOI: 10.3969/j.issn.1672-1454.2012.01.035 |
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| Authors: | WANG Min-hui LIU Guo-qing ZHANG Yin-long |
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| Affiliation: | 1.Harbin Normal University,School of Mathematical Sciences,Harbin 150300,China; 2.Harbin Institute of Technology,Department of Mathematics,Harbin 150006,China; 3.Armored force Institute of Technology,Department of Mathematics,Changchun 130117,China) |
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| Abstract: | We present various proofs on a variance formula Var max(a,X)≤VarX,based on properties of variance,covariance and convexity. |
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| Keywords: | variance covariance independent identical distribution convex function |
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