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A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice; it may also represent uncertainty, such as measurement error. However, the interpretation of probability is philosophically complicated, and even in specific cases is not always straightforward. The purely mathematical analysis of random variables is independent of such interpretational difficulties, and can be based upon a rigorous axiomatic setup.

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rdf:type	Thing
rdfs:label	Random variable (en)
rdfs:comment	A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice; it may also represent uncertainty, such as measurement error. However, the interpretation of probability is philosophically complicated, and even in specific cases is not always straightforward. The purely mathematical analysis of random variables is independent of such interpretational difficulties, and can be based upon a rigorous axiomatic setup. (en)
sameAs	Random variable Random variable
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Subject	Statistical randomness
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has abstract	A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice; it may also represent uncertainty, such as measurement error. However, the interpretation of probability is philosophically complicated, and even in specific cases is not always straightforward. The purely mathematical analysis of random variables is independent of such interpretational difficulties, and can be based upon a rigorous axiomatic setup. In the formal mathematical language of measure theory, a random variable is defined as a measurable function from a probability measure space (called the sample space) to a measurable space. This allows consideration of the pushforward measure, which is called the distribution of the random variable; the distribution is thus a probability measure on the set of all possible values of the random variable. It is possible for two random variables to have identical distributions but to differ in significant ways; for instance, they may be independent. It is common to consider the special cases of discrete random variables and continuous random variables, corresponding to whether a random variable is valued in a discrete set (such as a finite set) or in an interval of real numbers. There are other important possibilities, especially in the theory of stochastic processes, wherein it is natural to consider random sequences or random functions. Sometimes a random variable is taken to be automatically valued in the real numbers, with more general random quantities instead being called random elements. According to George Mackey, Pafnuty Chebyshev was the first person "to think systematically in terms of random variables". (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Random_variable
is Wikipage redirect of	Discrete random variable Aleatory variable Stochastic variable Random Variable Random variables RandomVariable Random quantity Random variation Equal in distribution Statistical variable Discrete Random Variable
is Link from a Wikipage to another Wikipage of	Flory–Huggins solution theory Flow-based generative model Flow (mathematics) Folded normal distribution Force of mortality Fractional social choice Franck Barthe Greek letters used in mathematics, science, and engineering List of statistics articles Locally convex topological vector space Location–scale family Log-Cauchy distribution Log-Laplace distribution Log-logistic distribution Log-normal distribution Logarithm Logarithmic distribution Logarithmically concave function Logistic distribution Logistic regression Logit-normal distribution Machine learning No free lunch in search and optimization Nonparametric skew Normal-gamma distribution Normal-inverse Gaussian distribution Normal distribution Normality test Evidence lower bound (a,b,0) class of distributions 18XX 1937 in science 68–95–99.7 rule Absorbing set (random dynamical systems) Actuarial notation Actuarial reserves Adapted process Addition Additive Markov chain Aleatoricism Algebra of random variables Algebraic statistics Algorithmic Lovász local lemma Algorithmic cooling Algorithmic inference Alternating conditional expectations An Essay towards solving a Problem in the Doctrine of Chances Analysis of variance Anderson's theorem Anil Kumar Bhattacharyya Anscombe transform Anton Formann Arbitrarily varying channel Areas of mathematics

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