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| {{StatsTopicTOC}}
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| The following is a [[glossary]] of terms used in the [[mathematics|mathematical]] sciences [[statistics]] and [[probability]].
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| {{term|term=Atomic event|content=[[Elementary event|Atomic event]]}}
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| {{defn|1=Another name for elementary event}}
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| {{term|term=Bias|content=[[Bias (statistics)|Bias]]}}
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| {{defn|no=1|A sample that is not representative of the population}}
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| {{defn|no=2|The difference between the expected value of an estimator and the true value}}
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| {{term|term=Binary data|content=[[Binary data]]}}
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| {{defn|1=Data that can take only two values, usually represented by 0 and 1}}
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| {{term|term=Conditional distribution|content=[[Conditional distribution]]}}
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| {{defn|1=Given two jointly distributed random variables ''X'' and ''Y'', the conditional probability distribution of ''Y'' given ''X'' (written "''Y'' <nowiki>|</nowiki> ''X''") is the probability distribution of ''Y'' when ''X'' is known to be a particular value}}
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| {{term|term=Conditional probability|content=[[Conditional probability]]}}
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| {{defn|1=The probability of some event A, assuming event B. Conditional probability is written P(''A''<nowiki>|</nowiki>''B''), and is read "the probability of ''A'', given ''B''"}}
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| {{term|term=Correlation|content=[[Correlation]]}}
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| {{defn|1=Also called correlation coefficient, a numeric measure of the strength of linear relationship between two random variables (one can use it to quantify, for example, how shoe size and height are correlated in the population). An example is the [[Pearson product-moment correlation coefficient]], which is found by dividing the covariance of the two variables by the product of their standard deviations. Independent variables have a correlation of 0}}
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| {{term|term=Count data|content=[[Count data]]}}
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| {{defn|1=Data arising from [[Counting]] that can take only non-negative integer values}}
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| {{term|term=Covariance|content=[[Covariance]]}}
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| {{defn|1=Given two random variables ''X'' and ''Y'', with expected values <math>E(X)=\mu</math> and <math>E(Y)=\nu</math>, covariance is defined as the expected value of random variable <math>(X - \mu) (Y - \nu)</math>, and is written <math>\operatorname{cov}(X, Y)</math>. It is used for measuring correlation}}
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| {{term|term=Credence|content=[[Credence (probability theory)|Credence]]}}
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| {{defn|1=A subjective estimate of probability}}
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| {{term|term=Data set|content=[[Data set]]}}
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| {{defn|1=A sample and the associated ''data points''}}
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| {{term|term=Data point|content=[[Data point]]}}
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| {{defn|1=A typed measurement — it can be a [[Boolean data type|Boolean]] value, a real number, a vector (in which case it's also called a data vector), etc}}
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| {{term|term=Elementary event|content=[[Elementary event]]}}
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| {{defn|1=An event with only one element. For example, when pulling a card out of a deck, "getting the jack of spades" is an elementary event, while "getting a king or an ace" is not}}
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| {{term|term=Estimator|content=[[Estimator]]}}
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| {{defn|1=A function of the known data that is used to estimate an unknown parameter; an estimate is the result from the actual application of the function to a particular set of data. The mean can be used as an estimator}}
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| {{term|term=Expected value|content=[[Expected value]]}}
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| {{term|Expectation}}
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| {{defn|1=The sum of the probability of each possible outcome of the experiment multiplied by its payoff ("value"). Thus, it represents the average amount one "expects" to win per bet if bets with identical odds are repeated many times. For example, the expected value of a six-sided die roll is 3.5. The concept is similar to the mean. The expected value of random variable ''X'' is typically written E(X) or <math>\mu</math> ([[Mu (letter)|mu]])}}
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| {{term|term=Experiment|content=[[Experiment (probability theory)|Experiment]]}}
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| {{defn|1=Any procedure that can be infinitely repeated and has a well-defined set of outcomes}}
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| {{term|term=Event|content=[[Event (probability theory)|Event]]}}
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| {{defn|1=A subset of the sample space (a possible experiment's outcome), to which a probability can be assigned. For example, on rolling a die, "getting a five or a six" is an event (with a probability of one third if the die is fair)}}
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| {{term|term=Joint distribution|content=[[Joint distribution]]}}
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| {{defn|1=Given two random variables ''X'' and ''Y'', the joint distribution of ''X'' and ''Y'' is the probability distribution of X and Y together}}
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| {{term|term=Joint probability|content=[[Joint probability]]}}
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| {{defn|1=The probability of two events occurring together. The joint probability of ''A'' and ''B'' is written <math>P(A \cap B)</math> or <math>P(A, \ B).</math>}}
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| {{term|term=Kurtosis|content=[[Kurtosis]]}}
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| {{defn|1=A measure of the "peakedness" of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations, as opposed to frequent modestly sized deviations}}
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| {{term|term=Likelihood function|content=[[Likelihood function]]}}
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| {{defn|1=A conditional probability function considered a function of its second argument with its first argument held fixed. For example, imagine pulling a numbered ball with the number k from a bag of n balls, numbered 1 to n. Then you could describe a likelihood function for the random variable N as the probability of getting k given that there are n balls : the likelihood will be 1/n for n greater or equal to k, and 0 for n smaller than k. Unlike a probability distribution function, this likelihood function will not sum up to 1 on the sample space}}
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| {{term|term=Marginal distribution|content=[[Marginal distribution]]}}
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| {{defn|1=Given two jointly distributed random variables ''X'' and ''Y'', the marginal distribution of ''X'' is simply the probability distribution of ''X'' ignoring information about ''Y''}}
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| {{term|term=Marginal probability|content=[[Marginal probability]]}}
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| {{defn|1=The probability of an event, ignoring any information about other events. The marginal probability of ''A'' is written ''P''(''A''). Contrast with conditional probability}}
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| {{term|term=Mean|content=[[Mean]]}}
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| {{defn|1=The expected value of a random variable}}
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| {{term|term=Multivariate random variable|content=[[Multivariate random variable]]}}
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| {{defn|1=A vector whose components are random variables on the same probability space}}
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| {{term|term=Mutual independence|content=[[Mutual independence]]}}
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| {{defn|1=A collection of events is mutually independent if for any subset of the collection, the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-flips. This is a stronger condition than pairwise independence}}
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| {{term|term=Pairwise independence|content=[[Pairwise independence]]}}
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| {{defn|1=A pairwise independent collection of random variables is a set of random variables any two of which are independent}}
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| {{term|term=Parameter|content=[[Statistical parameter|Parameter]] or Statistical parameter}}
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| {{defn|1=Can be a population parameter, a distribution parameter, an unobserved parameter (with different shades of meaning). In statistics, this is often a quantity to be estimated}}
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| {{term|term=Prior probability|content=[[Prior probability]]}}
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| {{defn|1=In [[Bayesian inference]], this represents prior beliefs or other information that is available before new data or observations are taken into account}}
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| {{term|term=Population parameter|content=[[Population parameter]]}}
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| {{defn|1=See statistical parameter}}
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| {{term|term=Posterior probability|content=[[Posterior probability]]}}
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| {{defn|1=The result of a [[Bayesian analysis]] that encapsulates the combination of prior beliefs or information with observed data}}
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| {{term|term=Probability density|content=[[Probability density function|Probability density]]}}
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| {{defn|1=Describes the probability in a continuous probability distribution. For example, you can't say that the probability of a man being six feet tall is 20%, but you can say he has 20% of chances of being between five and six feet tall. Probability density is given by a probability density function. Contrast with probability mass}}
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| {{term|term=Probability density function|content=[[Probability density function]]}}
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| {{defn|1=Gives the probability distribution for a continuous random variable}}
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| {{term|term=Probability distribution|content=[[Probability distribution]]}}
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| {{defn|1=A function that gives the probability of all elements in a given space: see [[List of probability distributions]]}}
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| {{term|term=Probability measure|content=[[Probability measure]]}}
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| {{defn|1=The probability of events in a probability space}}
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| {{term|term=Probability space|content=[[Probability space]]}}
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| {{defn|1=A sample space over which a probability measure has been defined}}
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| {{term|term=Random variable|content=[[Random variable]]}}
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| {{defn|1=A measurable function on a probability space, often real-valued. The distribution function of a random variable gives the probability of different results. We can also derive the mean and variance of a random variable}}
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| {{see also|Discrete random variable|Continuous random variable}}
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| {{term|term=Range|content=[[Range (statistics)|Range]]}}
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| {{defn|1=The length of the smallest interval which contains all the data}}
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| {{term|term=Sample|content=[[Statistical sample|Sample]]}}
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| {{defn|1=That part of a population which is actually observed}}
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| {{term|term=Sample space|content=[[Sample space]]}}
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| {{defn|1=The set of possible outcomes of an experiment. For example, the sample space for rolling a six-sided die will be <nowiki>{1, 2, 3, 4, 5, 6}</nowiki>}}
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| {{term|term=Sampling|content=[[Sampling (statistics)|Sampling]]}}
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| {{defn|1=A process of selecting observations to obtain knowledge about a population. There are many methods to choose on which sample to do the observations}}
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| {{term|term=Sampling distribution|content=[[Sampling distribution]]}}
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| {{defn|1=The probability distribution, under repeated sampling of the population, of a given statistic}}
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| {{term|term=Skewness|content=[[Skewness]]}}
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| {{defn|1=A measure of the asymmetry of the probability distribution of a real-valued random variable. Roughly speaking, a distribution has positive skew (right-skewed) if the higher tail is longer and negative skew (left-skewed) if the lower tail is longer (confusing the two is a common error)}}
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| {{term|term=Standard deviation|content=[[Standard deviation]]}}
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| {{defn|1=The most commonly used measure of statistical dispersion. It is the [[Square root]] of the variance, and is generally written <math>\sigma</math> ([[Sigma (letter)|Sigma]])}}
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| {{term|term=Statistic|content=[[Statistic]]}}
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| {{defn|1=The result of applying a statistical algorithm to a data set. It can also be described as an observable random variable}}
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| {{term|term=Statistical independence|content=[[Statistical independence]]}}
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| {{defn|1=Two events are independent if the outcome of one does not affect that of the other (for example, getting a 1 on one die roll does not affect the probability of getting a 1 on a second roll). Similarly, when we assert that two random variables are independent, we intuitively mean that knowing something about the value of one of them does not yield any information about the value of the other}}
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| {{term|term=Statistical inference|content=[[Statistical inference]]}}
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| {{defn|1=Inference about a population from a random sample drawn from it or, more generally, about a random process from its observed behavior during a finite period of time}}
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| {{term|term=Statistical population|content=[[Statistical population]]}}
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| {{defn|1=A set of entities about which statistical inferences are to be drawn, often based on random sampling. One can also talk about a population of measurements or values}}
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| {{term|term=Statistical dispersion|content=[[Statistical dispersion]]}}
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| {{defn|1=Statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation}}
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| {{term|term=Statistical parameter|content=[[Statistical parameter]]}}
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| {{defn|1=A parameter that indexes a family of probability distributions}}
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| {{term|term=Trial|content=[[Experiment (probability theory)|Trial]]}}
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| {{defn|1=Can refer to each individual repetition when talking about an experiment composed of any fixed number of them. As an example, one can think of an experiment being any number from one to ''n'' coin tosses, say 17. In this case, one toss can be called a trial to avoid confusion, since the whole experiment is composed of 17 ones. }}
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| {{term|term=Variance|content=[[Variance]]}}
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| {{defn|1=A measure of its statistical dispersion of a random variable, indicating how far from the expected value its values typically are. The variance of random variable ''X'' is typically designated as <math>\operatorname{var}(X)</math>, <math>\sigma_X^2</math>, or simply <math>\sigma^2</math>}}
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| {{glossend}}
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| == See also ==
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| * [[Notation in probability and statistics]]
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| * [[Probability axioms]]
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| * [[Glossary of experimental design]]
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| * [[List of statistical topics]]
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| * [[List of probability topics]]
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| == External links ==
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| * {{citation | title = NIST/SEMATECH e-Handbook of Statistical Methods | chapter = A Glossary of DOE Terminology | url = http://www.itl.nist.gov/div898/handbook/pri/section7/pri7.htm | publisher= [[NIST]] | accessdate = 28 February 2009}}
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| * {{ citation | url = http://www.statistics.com/resources/glossary/ | title = Statistical glossary | publisher = "statistics.com" | accessdate = 28 February 2009}}
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| * [http://www.economics.soton.ac.uk/staff/aldrich/Probability%20Earliest%20Uses.htm Probability and Statistics on the Earliest Uses Pages (Univ. of Southampton)]
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| [[Category:Probability and statistics| ]]
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| [[Category:Statistics-related lists]]
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| [[Category:Glossaries of science]]
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| [[Category:Glossaries of mathematics|Probability and statistics]]
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