In mathematics, probability, and statistics, a multivariate random variable or random vector is a list of mathematical variables each of whose values is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value. The individual variables in a random vector are grouped together because there may be correlations among them — often they represent different properties of an individual statistical unit (e.g. a particular person, event, etc.). Normally each element of a random vector is a real number.
Random vectors are often used as the underlying implementation of various types of aggregate random variables, e.g. a random matrix, random tree, random sequence, random process, etc.
More formally, a multivariate random variable is a column vector X = (X1, ..., Xn)T (or its transpose, which is a row vector) whose components are scalar-valued random variables on the same probability space (Ω, P), where Ω is the sample space, is the sigma-algebra (the collection of all events), and P is the probability measure (a function returning every event's probability).
Read more about Multivariate Random Variable: Probability Distribution, Operations On Random Vectors, Expected Value, Covariance, and Cross-covariance
Famous quotes containing the words random and/or variable:
“Man always made, and still makes, grotesque blunders in selecting and measuring forces, taken at random from the heap, but he never made a mistake in the value he set on the whole, which he symbolized as unity and worshipped as God. To this day, his attitude towards it has never changed, though science can no longer give to force a name.”
—Henry Brooks Adams (1838–1918)
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—Edmund Spenser (1552?–1599)