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| {{ProbabilityTopicsTOC}}
| | Floor Finisher Vancamp from Clarence Creek, usually spends time with interests including squash, [http://daphneandshamil.com/?option=com_k2&view=itemlist&task=user&id=30328 commercial property for sale] developers in singapore and scrabble. Likes to visit new destinations for example Generalife and Albayzín. |
| {{StatsTopicTOC}}
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| [[Probability theory]] and [[statistics]] have some commonly used conventions, in addition to standard [[mathematical notation]] and [[Table of mathematical symbols|mathematical symbols]].
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| ==Probability theory==
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| * [[Random variable]]s are usually written in [[upper case]] roman letters: ''X'', ''Y'', etc.
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| * Particular realizations of a random variable are written in corresponding [[lower case]] letters. For example ''x''<sub>1</sub>, ''x''<sub>2</sub>, …, ''x''<sub>''n''</sub> could be a [[random sample|sample]] corresponding to the random variable ''X''.
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| *<math>P(A \cap B)</math> or <math>P[A \cap B]</math> indicates the probability that events ''A'' and ''B'' both occur.
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| *<math>P(A \cup B)</math> or <math>P[A \cup B]</math> indicates the probability of either event ''A'' or event ''B'' occurring ("or" in this case means [[inclusive or|one or the other or both]]).
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| *[[sigma-algebra|σ-algebras]] are usually written with upper case [[Calligraphy|calligraphic]] (e.g. <math>\mathcal F</math> for the set of sets on which we define the probability ''P'')
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| *[[Probability density function]]s (pdfs) and [[probability mass function]]s are denoted by lower case letters, e.g. ''f''(''x'').
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| *[[Cumulative distribution function]]s (cdfs) are denoted by upper case letters, e.g. ''F''(''x'').
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| *In particular, the pdf of the [[standard normal distribution]] is denoted by φ(''z''), and its cdf by Φ(''z'').
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| *Some common operators:
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| :* E[''X''] : [[expected value]] of ''X''
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| :* var[''X''] : [[variance]] of ''X''
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| :* cov[''X'', ''Y''] : [[covariance]] of ''X'' and ''Y''
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| ==Statistics==
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| *Greek letters (e.g. θ, β) are commonly used to denote unknown parameters (population parameters).
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| *An [[estimator|estimate]] of a parameter is often denoted by placing a [[caret]] or "hat" over the corresponding symbol, e.g. <math>\hat{\theta}</math>, pronounced "theta hat".
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| *The [[arithmetic mean]] of a series of values ''x''<sub>1</sub>, ''x''<sub>2</sub>, ..., ''x''<sub>''n''</sub> is often denoted by placing an "[[overbar]]" over the symbol, e.g. <math>\bar{x}</math>, pronounced "''x'' bar".
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| *Some commonly used symbols for [[Sample (statistics)|sample]] statistics are given below:
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| **the [[sample mean]] <math>\bar{x}</math>,
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| **the [[sample variance]] ''s''<sup>2</sup>,
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| ** the [[sample standard deviation]] ''s'',
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| **the [[Pearson correlation coefficient|sample correlation coefficient]] ''r'',
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| **the sample cumulants ''k<sub>r</sub>''.
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| *Some commonly used symbols for [[Statistical population|population]] parameters are given below:
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| **the population mean ''μ'',
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| **the population variance ''σ''<sup>2</sup>,
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| ** the population standard deviation ''σ'',
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| **the population [[Pearson product-moment correlation coefficient|correlation]] ''ρ'',
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| **the population [[cumulant]]s ''κ<sub>r</sub>''.
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| ==Critical values==
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| The α-level upper [[critical value]] of a [[probability distribution]] is the value exceeded with probability α, that is, the value ''x''<sub>α</sub> such that ''F''(''x''<sub>α</sub>) = 1 − α where ''F'' is the cumulative distribution function. There are standard notations for the upper critical values of some commonly used distributions in statistics:
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| *''z''<sub>α</sub> or ''z''(α) for the [[Standard normal distribution]]
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| *''t''<sub>α,ν</sub> or ''t''(α,ν) for the [[t-distribution]] with ν [[Degrees of freedom (statistics)|degrees of freedom]]
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| *<math>\chi^2_{\alpha,\nu}</math> or <math>\chi^2(\alpha,\nu)</math> for the [[chi-squared distribution]] with ν degrees of freedom
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| *<math>F_{\alpha,\nu_1,\nu_2}</math> or F(α,ν<sub>1</sub>,ν<sub>2</sub>) for the [[F-distribution]] with ν<sub>1</sub> and ν<sub>2</sub> degrees of freedom
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| ==Linear algebra== | |
| *[[Matrix (mathematics)|Matrices]] are usually denoted by boldface capital letters, e.g. '''A'''.
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| *[[Column vector]]s are usually denoted by boldface lower case letters, e.g. '''x'''.
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| *The [[transpose]] operator is denoted by either a superscript T (e.g. '''A'''<sup>T</sup>) or a [[prime (symbol)|prime symbol]] (e.g. '''A'''′).
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| *A [[row vector]] is written as the transpose of a column vector, e.g. '''x'''<sup>T</sup> or '''x'''′.
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| ==Abbreviations== | |
| Common abbreviations include:
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| *'''a.e.''' [[almost everywhere]]
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| *'''a.s.''' [[almost surely]]
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| * '''cdf''' [[cumulative distribution function]]
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| * '''cmf''' [[cumulative mass function]]
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| *'''df''' [[degrees of freedom (statistics)|degrees of freedom]] (also <math>\nu</math>)
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| *'''i.i.d.''' [[Independent and identically distributed random variables|independent and identically distributed]]
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| *'''pdf''' [[probability density function]]
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| *'''pmf''' [[probability mass function]]
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| * '''r.v.''' [[random variable]]
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| * '''w.p.''' [[with probability]]; '''wp1''' [[with probability 1]]
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| == See also ==
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| *[[Glossary of probability and statistics]]
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| *[[Combinations and permutations]]
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| *[[Typographical conventions in mathematical formulae]]
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| *[[History of mathematical notation]]
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| ==References==
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| *{{Citation| title=Recommended Standards for Statistical Symbols and Notation. COPSS Committee on Symbols and Notation| first1=Max|last1=Halperin |first2=H. O. |last2=Hartley |first3=P. G.|last3=Hoel | journal=The American Statistician| volume=19 |year=1965 | pages=12–14 | issue=3| doi=10.2307/2681417 | jstor=2681417}}
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| ==External links==
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| *[http://jeff560.tripod.com/stat.html Earliest Uses of Symbols in Probability and Statistics], maintained by Jeff Miller.
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| [[Category:Probability and statistics]]
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| [[Category:Mathematical notation]]
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| [[Category:Statistical terminology]]
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Floor Finisher Vancamp from Clarence Creek, usually spends time with interests including squash, commercial property for sale developers in singapore and scrabble. Likes to visit new destinations for example Generalife and Albayzín.