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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 Notation in probability and statistics ： ウィキペディア英語版 Notation in probability and statistics Probability theory and statistics have some commonly used conventions, in addition to standard mathematical notation and mathematical symbols. ==Probability theory== * Random variables are usually written in upper case roman letters: ''X'', ''Y'', etc. * Particular realizations of a random variable are written in corresponding lower case letters. For example ''x''1, ''x''2, …, ''x''''n'' could be a sample corresponding to the random variable ''X'' and a cumulative probability is formally written $P(X>x)$ to differentiate random variable from realization. * The probability is sometimes written $\backslash mathbb$ to distinguish it from other functions and measure ''P'' so as to avoid having to define " ''P'' is a probability" and $\backslash mathbb(A)$ is short for $P(\backslash )$, where $\backslash omega$ is an event and $X(\backslash omega)$ a corresponding random variable. *$\backslash mathbb(A\; \backslash cap\; B)$ or $\backslash mathbb(\backslash cap\; B)$ indicates the probability that events ''A'' and ''B'' both occur. *$\backslash mathbb(A\; \backslash cup\; B)$ or $\backslash mathbb(\backslash cup\; B)$ indicates the probability of either event ''A'' or event ''B'' occurring ("or" in this case means one or the other or both). *σ-algebras are usually written with upper case calligraphic (e.g. $\backslash mathcal\; F$ for the set of sets on which we define the probability ''P'') *Probability density functions (pdfs) and probability mass functions are denoted by lower case letters, e.g. ''f''(''x''). *Cumulative distribution functions (cdfs) are denoted by upper case letters, e.g. ''F''(''x''). * Survival functions or complementary cumulative distribution functions are often denoted by placing an overbar over the symbol for the cumulative:$\backslash overline(x)\; =1-F(x)$ *In particular, the pdf of the standard normal distribution is denoted by φ(''z''), and its cdf by Φ(''z''). *Some common operators: : * E() : expected value of ''X'' : * var() : variance of ''X'' : * cov(''Y'' ) : covariance of ''X'' and ''Y'' * X is independent of Y is often written $X\; \backslash perp\; Y$ or $X\; \backslash perp\backslash !\backslash !\backslash !\backslash perp\; Y$, and X is independent of Y given W is often written :$X\; \backslash perp\backslash !\backslash !\backslash !\backslash perp\; Y\; \backslash ,|\backslash ,\; W$ or :$X\; \backslash perp\; Y\; \backslash ,|\backslash ,\; W$ * $\backslash textstyle\; P(A\backslash mid\; B)$, the ''posterior probability'', is the probability of $\backslash textstyle\; A$ ''given'' $\backslash textstyle\; B$, i.e., ''after'' $\backslash textstyle\; B$ is observed. 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「Notation in probability and statistics」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.