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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 Gauss's inequality ： ウィキペディア英語版 Gauss's inequality In probability theory, Gauss's inequality (or the Gauss inequality) gives an upper bound on the probability that a unimodal random variable lies more than any given distance from its mode. Let ''X'' be a unimodal random variable with mode ''m'', and let ''τ'' 2 be the expected value of (''X'' − ''m'')2. (''τ'' 2 can also be expressed as (''μ'' − ''m'')2 + ''σ'' 2, where ''μ'' and ''σ'' are the mean and standard deviation of ''X''.) Then for any positive value of ''k'', :$$ \Pr(\mid X - m \mid > k) \leq \begin \left( \frac \right)^2 & \text k \geq \frac 0 \leq k \leq \frac The theorem was first proved by Carl Friedrich Gauss in 1823. ==See also== *Vysochanskiï–Petunin inequality, a similar result for the distance from the mean rather than the mode *Chebyshev's inequality, concerns distance from the mean without requiring unimodality 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「Gauss's 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.