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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Concentration inequality ： ウィキペディア英語版 Concentration inequality In mathematics, concentration inequalities provide probability bounds on how a random variable deviates from some value (e.g., its expectation). The laws of large numbers of classical probability theory state that sums of independent random variables are, under very mild conditions, close to their expectation with a large probability. Such sums are the most basic examples of random variables concentrated around their mean. Recent results shows that such behavior is shared by other functions of independent random variables. ==Markov's inequality== If ''X'' is a nonnegative random variable and ''a'' > 0, then : $\backslash Pr(X\; \backslash geq\; a)\; \backslash leq\; \backslash frac.$ Proof can be found here. We can extend Markov's inequality to a strictly increasing and non-negative function $\backslash Phi$. We have :$\backslash Pr(X\; \backslash geq\; a)\; =\; \backslash Pr(\backslash Phi\; (X)\; \backslash geq\; \backslash Phi\; (a))\; \backslash leq\; \backslash frac.$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Concentration inequality」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.