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- Glossary_of_probability_and_statistics abstract "The following is a glossary of terms used in the mathematical sciences statistics and probability. Atomic eventAnother name for elementary eventBias1. A sample that is not representative of the population2. The difference between the expected value of an estimator and the true valueBinary dataData that can take only two values, usually represented by 0 and 1Conditional distributionGiven two jointly distributed random variables X and Y, the conditional probability distribution of Y given X (written "Y | X") is the probability distribution of Y when X is known to be a particular valueConditional probabilityThe probability of some event A, assuming event B. Conditional probability is written P(A|B), and is read "the probability of A, given B"CorrelationAlso 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 0Count dataData arising from Counting that can take only non-negative integer valuesCovarianceGiven two random variables X and Y, with expected values and , covariance is defined as the expected value of random variable , and is written . It is used for measuring correlationCredenceA subjective estimate of probabilityData setA sample and the associated data pointsData pointA typed measurement — it can be a Boolean value, a real number, a vector (in which case it's also called a data vector), etcElementary eventAn 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 notEstimatorA 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 estimatorExpected valueExpectationThe 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 (mu)ExperimentAny procedure that can be infinitely repeated and has a well-defined set of outcomesEventA 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)Joint distributionGiven two random variables X and Y, the joint distribution of X and Y is the probability distribution of X and Y togetherJoint probabilityThe probability of two events occurring together. The joint probability of A and B is written or KurtosisA 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 deviationsLikelihood functionA 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 spaceMarginal distributionGiven two jointly distributed random variables X and Y, the marginal distribution of X is simply the probability distribution of X ignoring information about YMarginal probabilityThe probability of an event, ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probabilityMeanThe expected value of a random variableMultivariate random variableA vector whose components are random variables on the same probability spaceMutual independenceA 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 independencePairwise independenceA pairwise independent collection of random variables is a set of random variables any two of which are independentParameter or Statistical parameterCan be a population parameter, a distribution parameter, an unobserved parameter (with different shades of meaning). In statistics, this is often a quantity to be estimatedPrior probabilityIn Bayesian inference, this represents prior beliefs or other information that is available before new data or observations are taken into accountPopulation parameterSee statistical parameterPosterior probabilityThe result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed dataProbability densityDescribes 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 massProbability density functionGives the probability distribution for a continuous random variableProbability distributionA function that gives the probability of all elements in a given space: see List of probability distributionsProbability measureThe probability of events in a probability spaceProbability spaceA sample space over which a probability measure has been definedRandom variableA 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 variableRangeThe length of the smallest interval which contains all the dataSampleThat part of a population which is actually observedSample spaceThe set of possible outcomes of an experiment. For example, the sample space for rolling a six-sided die will be {1, 2, 3, 4, 5, 6}SamplingA process of selecting observations to obtain knowledge about a population. There are many methods to choose on which sample to do the observationsSampling distributionThe probability distribution, under repeated sampling of the population, of a given statisticSkewnessA 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)Standard deviationThe most commonly used measure of statistical dispersion. It is the Square root of the variance, and is generally written (Sigma)StatisticThe result of applying a statistical algorithm to a data set. It can also be described as an observable random variableStatistical independenceTwo 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 otherStatistical inferenceInference 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 timeStatistical populationA 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 valuesStatistical dispersionStatistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviationStatistical parameterA parameter that indexes a family of probability distributionsTrialCan 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.VarianceA 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 , , or simply </dl>".
- Glossary_of_probability_and_statistics wikiPageExternalLink Probability%20Earliest%20Uses.htm.
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- Glossary_of_probability_and_statistics wikiPageExternalLink glossary.
- Glossary_of_probability_and_statistics wikiPageID "2142850".
- Glossary_of_probability_and_statistics wikiPageRevisionID "549756802".
- Glossary_of_probability_and_statistics content Bias_(statistics).
- Glossary_of_probability_and_statistics content Binary_data.
- Glossary_of_probability_and_statistics content Conditional_probability.
- Glossary_of_probability_and_statistics content Conditional_probability_distribution.
- Glossary_of_probability_and_statistics content Correlation_and_dependence.
- Glossary_of_probability_and_statistics content Count_data.
- Glossary_of_probability_and_statistics content Covariance.
- Glossary_of_probability_and_statistics content Data_point.
- Glossary_of_probability_and_statistics content Data_set.
- Glossary_of_probability_and_statistics content Elementary_event.
- Glossary_of_probability_and_statistics content Estimator.
- Glossary_of_probability_and_statistics content Event_(probability_theory).
- Glossary_of_probability_and_statistics content Expected_value.
- Glossary_of_probability_and_statistics content Experiment_(probability_theory).
- Glossary_of_probability_and_statistics content Independence_(probability_theory).
- Glossary_of_probability_and_statistics content Joint_probability_distribution.
- Glossary_of_probability_and_statistics content Kurtosis.
- Glossary_of_probability_and_statistics content Likelihood_function.
- Glossary_of_probability_and_statistics content Marginal_distribution.
- Glossary_of_probability_and_statistics content Mean.
- Glossary_of_probability_and_statistics content Multivariate_random_variable.
- Glossary_of_probability_and_statistics content Pairwise_independence.
- Glossary_of_probability_and_statistics content Posterior_probability.
- Glossary_of_probability_and_statistics content Prior_probability.
- Glossary_of_probability_and_statistics content Probability_density_function.
- Glossary_of_probability_and_statistics content Probability_distribution.
- Glossary_of_probability_and_statistics content Probability_measure.
- Glossary_of_probability_and_statistics content Probability_space.
- Glossary_of_probability_and_statistics content Random_variable.
- Glossary_of_probability_and_statistics content Range_(statistics).
- Glossary_of_probability_and_statistics content Sample_(statistics).
- Glossary_of_probability_and_statistics content Sample_space.
- Glossary_of_probability_and_statistics content Sampling_(statistics).
- Glossary_of_probability_and_statistics content Sampling_distribution.
- Glossary_of_probability_and_statistics content Skewness.
- Glossary_of_probability_and_statistics content Standard_deviation.
- Glossary_of_probability_and_statistics content Statistic.
- Glossary_of_probability_and_statistics content Statistical_dispersion.
- Glossary_of_probability_and_statistics content Statistical_inference.
- Glossary_of_probability_and_statistics content Statistical_parameter.
- Glossary_of_probability_and_statistics content Statistical_population.
- Glossary_of_probability_and_statistics content Variance.
- Glossary_of_probability_and_statistics content "Parameter or Statistical parameter".
- Glossary_of_probability_and_statistics content Credence_(probability_theory).
- Glossary_of_probability_and_statistics hasPhotoCollection Glossary_of_probability_and_statistics.
- Glossary_of_probability_and_statistics term "Atomic event".
- Glossary_of_probability_and_statistics term "Bias".
- Glossary_of_probability_and_statistics term "Binary data".
- Glossary_of_probability_and_statistics term "Conditional distribution".
- Glossary_of_probability_and_statistics term "Conditional probability".
- Glossary_of_probability_and_statistics term "Correlation".
- Glossary_of_probability_and_statistics term "Count data".
- Glossary_of_probability_and_statistics term "Covariance".
- Glossary_of_probability_and_statistics term "Credence".
- Glossary_of_probability_and_statistics term "Data point".
- Glossary_of_probability_and_statistics term "Data set".
- Glossary_of_probability_and_statistics term "Elementary event".
- Glossary_of_probability_and_statistics term "Estimator".
- Glossary_of_probability_and_statistics term "Event".
- Glossary_of_probability_and_statistics term "Expected value".
- Glossary_of_probability_and_statistics term "Experiment".
- Glossary_of_probability_and_statistics term "Joint distribution".
- Glossary_of_probability_and_statistics term "Joint probability".
- Glossary_of_probability_and_statistics term "Kurtosis".
- Glossary_of_probability_and_statistics term "Likelihood function".
- Glossary_of_probability_and_statistics term "Marginal distribution".
- Glossary_of_probability_and_statistics term "Marginal probability".
- Glossary_of_probability_and_statistics term "Mean".
- Glossary_of_probability_and_statistics term "Multivariate random variable".
- Glossary_of_probability_and_statistics term "Mutual independence".
- Glossary_of_probability_and_statistics term "Pairwise independence".
- Glossary_of_probability_and_statistics term "Parameter".
- Glossary_of_probability_and_statistics term "Population parameter".
- Glossary_of_probability_and_statistics term "Posterior probability".
- Glossary_of_probability_and_statistics term "Prior probability".
- Glossary_of_probability_and_statistics term "Probability density function".
- Glossary_of_probability_and_statistics term "Probability density".
- Glossary_of_probability_and_statistics term "Probability distribution".
- Glossary_of_probability_and_statistics term "Probability measure".
- Glossary_of_probability_and_statistics term "Probability space".
- Glossary_of_probability_and_statistics term "Random variable".
- Glossary_of_probability_and_statistics term "Range".
- Glossary_of_probability_and_statistics term "Sample space".
- Glossary_of_probability_and_statistics term "Sample".
- Glossary_of_probability_and_statistics term "Sampling distribution".
- Glossary_of_probability_and_statistics term "Sampling".
- Glossary_of_probability_and_statistics term "Skewness".
- Glossary_of_probability_and_statistics term "Standard deviation".
- Glossary_of_probability_and_statistics term "Statistic".
- Glossary_of_probability_and_statistics term "Statistical dispersion".
- Glossary_of_probability_and_statistics term "Statistical independence".
- Glossary_of_probability_and_statistics term "Statistical inference".
- Glossary_of_probability_and_statistics term "Statistical parameter".
- Glossary_of_probability_and_statistics term "Statistical population".