Random Variable

A random variable is a measurable function from a probability space (S,S,P) into a measurable space (S^',S^') known as the state space (Doob 1996). Papoulis (1984, p. 88) gives the slightly different definition of a random variable X as a real function whose domain is the probability space S and such that:

1. The set {X<=x} is an event for any real number x.

2. The probability of the events {X=+infty} and {X=-infty} equals zero.

The abbreviation "r.v." is sometimes used to denote a random variable.

See also

Principle of Insufficient Reason, Probability Space, Random Distribution, Random Number, Random Variate, State Space, Variate

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References

Doob, J. L. "The Development of Rigor in Mathematical Probability (1900-1950)." Amer. Math. Monthly 103, 586-595, 1996.Evans, M.; Hastings, N.; and Peacock, B. Statistical Distributions, 3rd ed. New York: Wiley, 2000.Gikhman, I. I. and Skorokhod, A. V. Introduction to the Theory of Random Processes. New York: Dover, 1997.Papoulis, A. "The Concept of a Random Variable." Ch. 4 in Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 83-115, 1984.

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Random Variable

Cite this as:

Weisstein, Eric W. "Random Variable." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RandomVariable.html

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