Abstract
The standard situation in the modeling of a random phenomenon is that the quantities of interest, rather than being defined on the underlying probability space, are functions from the probability space to some other (measurable) space. These functions are called random variables. Strictly speaking, one uses the term random variable when they are functions from the probability space to ℝ. If the image is in ℝn for some n ≥ 2 one talks about n-dimensional random variables or simply random vectors. If the image space is a general abstract one, one talks about random elements.
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© 2005 Springer Science+Business Media, Inc.
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(2005). Random Variables. In: Probability: A Graduate Course. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/0-387-27332-8_2
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DOI: https://doi.org/10.1007/0-387-27332-8_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-22833-4
Online ISBN: 978-0-387-27332-7
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