Chebyshev's inequality
Chebyshev's inequality This article is not about Chebyshev's sum inequality. In probability theory, Chebyshev' ...
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Talk:Chebyshev's inequality
Talk:Chebyshev's inequality I wonder if we should rename this to "Chebyshev's inequality". First, Chebyshev seems to be ...
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Chebyshev's sum inequality
Chebyshev's sum inequality Another article treats Chebyshev's inequality in probability theory. In mathematics, ...
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Chebyshev's theorem
Chebyshev's theorem Chebyshev's theorem is a name given to several theorems proven by Russian mathematician Pafnuty Chebyshev: Bertrand's postulate Chebyshev's inequality ...
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Kolmogorov's inequality
Kolmogorov's inequality Kolmogorov's inequality is a mathematical inequality appearing in probability theory, named after ...
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Hoeffding's inequality
Hoeffding's inequality Hoeffding's inequality, named after Wassily Hoeffding, is a result ... for the sum of these variables $$S = X_1 + \ldots + X_n \! we have ...
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Markov's inequality
Markov's inequality In probability theory, Markov's inequality gives an upper bound for the probability ... after the Russian mathematician Andrey Markov. Markov's inequality (and other similar inequalities) relate ...
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Inequality
Inequality For the socioeconomic sense, see social inequality. The feasible regions of linear programming are ... a set of inequalities. In mathematics, an inequality is a statement about the relative size ... b. These relations are known as strict inequality; in contrast a ≤ b means that ... to b. If the sense of the inequality is the same for all values ...
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Pafnuty Chebyshev
Pafnuty Chebyshev Pafnuty Lvovich Chebyshev Pafnuty Lvovich Chebyshev (Пафну́т ... father was the wealthy landowner Lev Pavlovich Chebyshev. Pafnuty Lvovich got his first education at ... teacher also played an important role in Chebyshev's education, for she "brought up ...
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Rearrangement inequality
Rearrangement inequality Let $x\_1\; \backslash leq\; \backslash cdots\; \backslash leq\; x\_n\; ...\; x\_1,\; \backslash dots\; ,\; x\_n$. Then the rearrangement inequality states that $x\_1y\_1\; +\; \backslash cdots\; +\; x\_ny\_n\; \backslash geq\; ...\; geq\; x\_ny\_1\; +\; \backslash cdots\; +\; x\_1y\_n.$ The rearrangement inequality can be proved by induction. Many famous ... inequalities can be proved by the rearrangement inequality, such as the arithmetic mean - geometric mean inequality, the Cauchy-Schwartz inequality, and Chebyshev' ...
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