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{\displaystyle \textstyle \mathbb {R} }; it is a function defined from the set of possible outcomes of a random experiment, for which we must be able to determine the probability that it takes a given value or a given set of values. Real random variables are the most commonly studied random variables, which leads some authors to omit the adjective real, and to simply refer to a random variable.

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This article does not cite its sources sufficiently (September 2013).

Random variables are widely used in probability theory and statistics. In applications, random variables are used to model the outcome of a non-deterministic mechanism or as the result of a non-deterministic experiment that generates a random outcome. In mathematical or inferential statistics, random variables are generally used to model assumed infinite populations.

This article only deals with real random variables:

The article Random variable generalizes this article to the non-real case from the perspective of measure theory;

The article Elementary random variables addresses the concept of random variable in a more intuitive way.

An example of a random variable:

the function that associates the sum of the values of two dice to the outcome of rolling them.

Details

Some real random variables

Basic concepts

Practical tools

Simulation of a random variable

See also