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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 Random structure function ： ウィキペディア英語版 Random structure function The random structure function〔Elart von Collani, Defining and Modeling Uncertainty, ''Journal of Uncertainty Systems'', Vol. 2, 202−211, 2008, ().〕 is the third component of the Bernoulli space which constitutes the stochastic model within Bernoulli stochastics.〔Elart von Collani (ed.), ''Defining the Science Stochastics'', Heldermann Verlag, Lemgo, 2004.〕 The Bernoulli space describes the transition from past to future. The determinate past is represented by a variable ''D'' which is called deterministic variable, because its value is fixed. The future represented by the variable ''X'' is subject to randomness and ''X'' is therefore called random variable. The random variable ''X'' may adopt one of a set of different values according to a random law which depends on the actual initial conditions given by the value ''d'' of the deterministic variable. The random law does not only fix the range of variability of ''X'' but also the probability of the future events which are given by subsets of the range of variability of ''X''. ==Probability distribution== The random variable ''X'' stands for the future indeterminate outcome of a process. If the process is repeated then different outcomes will occur according to a random law that depends on the actual initial conditions given by the value ''d'' of the deterministic variable ''D''. The random variable ''X'' under the condition ''d'' is denoted $X|\backslash$ where the set of possible initial conditions is given by the ignorance space $\backslash mathfrak$. The random structure function assigns to each subset of the ignorance space a probability distribution. Let $\backslash mathfrak\_0$ be a subset of the ignorance space $\backslash mathfrak$ then the corresponding probability distribution is obtained from the images $\backslash mathfrak(\backslash )$ of the singletons $\backslash$ as follows: :::$\backslash mathfrak(\backslash mathfrak\_0))\; =\; \backslash frac\; \backslash sum\_\backslash mathfrak(\backslash )$ It follows that for any future event ''E'', we have: :::$P\_(E)\; =\; \backslash frac\; \backslash sum\_\; P\_\_0$ is given by the mean of the probability distributions of the random variables $X|\backslash$. 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「Random structure function」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.