Random Variable (original) (raw)
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A random variable is a measurable function from a probability space 
into a measurable space 
known as the state space (Doob 1996). Papoulis (1984, p. 88) gives the slightly different definition of a random variable 
as a real function whose domain is the probability space 
and such that:
1. The set 
is an event for any real number 
.
2. The probability of the events 
and 
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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Cite this as:
Weisstein, Eric W. "Random Variable." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RandomVariable.html