| 一常见不等式的推广及其概率意义 |
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| 引用本文： | 闻荣,侯为波.一常见不等式的推广及其概率意义[J].淮北煤炭师范学院学报(自然科学版),1998(3). |
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| 作者姓名： | 闻荣 侯为波 |
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| 作者单位： | 淮北煤师院附属实验中学(闻荣),西安交大理学院(侯为波) |
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| 摘 要： | 本文应用Jensen不等式证明了著名不等式：调和平均值≤几何平均值≤算术平均值．并将该不等式推广至非常一般的形式．文中给出该不等式所表示的概率意义,并用以解释日常生活中的一常见现象．
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| 关 键 词： | Jensen不等式 凸函数 数学期望 |
A Generalization and Probability Meaning of a Common Inequality |
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| Wen Rong, Hou Weibo.A Generalization and Probability Meaning of a Common Inequality[J].Journal of Huaibei Coal Industry Teachers College(Natural Science edition),1998(3). |
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| Authors: | Wen Rong Hou Weibo |
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| Institution: | Wen Rong; Hou Weibo (The High School Attoched to Huaibei Cool Normal College) (Xi'an Jiaotong University) |
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| Abstract: | A new prove method and a generalization of the famous inequality "harmonic mean-gemetric mean-arithmetic mean inequality" is given by means of Jensen Inequality in this paper.The probability meaning of geometric mean-arithmetic mean inequality is studied and used to explain a common phenomeron in agriculture. |
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| Keywords: | Jensen Inequality convex function mathematical expectation |
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