翻訳と辞書 Words near each other ・ Taylor Lilley ・ Taylor Lindsey ・ Taylor Lipsett ・ Taylor Locke and The Roughs ・ Taylor Log House and Site ・ Taylor Lord ・ Taylor Lytle ・ Taylor Mac ・ Taylor Mackenzie ・ Taylor Made Jazz ・ Taylor Edgar ・ Taylor Eigsti ・ Taylor Eisenhart ・ Taylor Energy ・ Taylor Even ・ Taylor expansions for the moments of functions of random variables ・ Taylor Farm ・ Taylor Farm (Richlands, North Carolina) ・ Taylor Farm (Richmond, Virginia) ・ Taylor Farms ・ Taylor Fashions Ltd v Liverpool Victoria Trustees Co Ltd ・ Taylor Featherston ・ Taylor Fedun ・ Taylor Ferry, Oklahoma ・ Taylor Field ・ Taylor Field (Airfield) ・ Taylor Field (Florida) ・ Taylor Fletcher ・ Taylor Forge ・ Taylor Forge Engineered Systems 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 Taylor expansions for the moments of functions of random variables ： ウィキペディア英語版 Taylor expansions for the moments of functions of random variables In probability theory, it is possible to approximate the moments of a function ''f'' of a random variable ''X'' using Taylor expansions, provided that ''f'' is sufficiently differentiable and that the moments of ''X'' are finite. This technique is often used by statisticians. ==First moment== : $$ \begin \operatorname\left() & \approx \operatorname\left(+ f'(\mu_X)\left(X-\mu_X\right) + \fracf''(\mu_X) \left(X - \mu_X\right)^2 \right ). \end Notice that $E()=0$, the 2nd term disappears. Also $E()$ is $\backslash sigma\_X^2$. Therefore, :$\backslash operatorname\backslash left()\backslash approx\; f(\backslash mu\_X)\; +\backslash frac\backslash sigma\_X^2$ where $\backslash mu\_X$ and $\backslash sigma^2\_X$ are the mean and variance of X respectively.〔Haym Benaroya, Seon Mi Han, and Mark Nagurka. ''Probability Models in Engineering and Science''. CRC Press, 2005.〕 It is possible to generalize this to functions of more than one variable using multivariate Taylor expansions. For example, :$\backslash operatorname\backslash left()\backslash approx\backslash frac\; -\backslash frac+\backslash frac\backslash operatorname\backslash left()$ 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「Taylor expansions for the moments of functions of 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.