切比雪夫不等式,Chebyshev's inequality

1)Chebyshev's inequality
切比雪夫不等式
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2)chebyshev inequality
切比雪夫不等式
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3)tchebycheff inequality
切比雪夫不等式
1.
We study in this paper the expectation, variance, independence and linear dependence of self-adjoint random variables on a noncommutative probability space, and prove Tchebycheff inequality and law of large numbers.
研究了非交换概率空间上自伴随机变量的期望、方差、独立性、相关性等性质,证明了关于自伴随机变量的切比雪夫不等式与大数定理。


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4)Chebyshev type inequality
切比雪夫型不等式
1.
In this paper,by means of some algebraic and analytical skills,the author gives a new proof for Chebyshev type inequality involving permanents perA/∏from i=1 to n ∑from j=1 to n ai,j≤perB/∏from i=1 to n ∑from j=1 to n bi,j Moreover,the author also gives an application of this result.
主旨是借助于代数和分析工具给出如下涉及积和式的切比雪夫型不等式perA/∏from i=1 to n ∑from j=1 to n ai,j≤perB/∏from i=1 to n ∑from j=1 to n bi,j的一个新证明,同时也展示了该结果的一个新的应用。



5)mean-value theorem for different
切比雪夫积分不等式
1.
In the article,a simple and elementary proof of monotonicity is given for the so-called extended mean values using Tchebycheff s integral inequality and the mean-value theorem for differential.
本文利用切比雪夫积分不等式和微分中值定理,对所谓的双参数拓广平均的单调递增性给出一种简单的证明。



6)the Chebyshev's Inequality
车比雪夫不等式


补充资料：契比雪夫不等式

对于n个正数a1~an以及b1~bn,有排序关系a1≤a2≤...≤an,b1≤b2≤...≤bn, 则有a1bn+a2b(n-1)+...+anb1≤1/n（a1+a2+...+an)(b1+b2+...+bn)≤a1b1+a2b2+..+anbn，该不等式即为契比雪夫不等式。

契比雪夫不等式实质上是排序不等式的一个推广。在除数学之外的其他领域也有广泛应用。

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切比雪夫不等式,Chebyshev's inequality