翻訳と辞書 Words near each other ・ Sum 41 discography ・ Sum activity of peripheral deiodinases ・ Sum addressed decoder ・ Sum Alahi Mong ・ Sum and Product Puzzle ・ Sum and Substance ・ Sum certain ・ Sum Elai-Mang ・ Sum frequency generation spectroscopy ・ Sum Mo Chikan ・ Sum of absolute differences ・ Sum of absolute transformed differences ・ Sum of angles of a triangle ・ Sum of Christianity ・ Sum of Logic ・ Sum of normally distributed random variables ・ Sum of Parts ・ Sum of perpetuities method ・ Sum of public power ・ Sum of radicals ・ Sum of squares ・ Sum of the Parts ・ Sum of two squares theorem ・ Sum Practysis of Medecyne and other Short Works ・ Sum rule ・ Sum rule in differentiation ・ Sum rule in integration ・ Sum rule in quantum mechanics ・ Sum to Infinity ・ Sum to Infinity (book) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Sum of normally distributed random variables ： ウィキペディア英語版 Sum of normally distributed random variables In probability theory, calculation of the sum of normally distributed random variables is an instance of the arithmetic of random variables, which can be quite complex based on the probability distributions of the random variables involved and their relationships. ==Independent random variables== If ''X'' and ''Y'' are independent random variables that are normally distributed (and therefore also jointly so), then their sum is also normally distributed. i.e., if :$X\; \backslash sim\; N(\backslash mu\_X,\; \backslash sigma\_X^2)$ :$Y\; \backslash sim\; N(\backslash mu\_Y,\; \backslash sigma\_Y^2)$ :$Z=X+Y,$ then :$Z\; \backslash sim\; N(\backslash mu\_X\; +\; \backslash mu\_Y,\; \backslash sigma\_X^2\; +\; \backslash sigma\_Y^2).$ This means that the sum of two independent normally distributed random variables is normal, with its mean being the sum of the two means, and its variance being the sum of the two variances (i.e., the square of the standard deviation is the sum of the squares of the standard deviations). Note that the result that the sum is normally distributed requires the assumption of independence, not just uncorrelatedness; two separately (not jointly) normally distributed random variables can be uncorrelated without being independent, in which case their sum can be non-normally distributed (see Normally distributed and uncorrelated does not imply independent#A symmetric example). The result about the mean holds in all cases, while the result for the variance requires uncorrelatedness, but not independence. 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「Sum of normally distributed random variables」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.