# random variable

## English

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### Noun

random variable (plural random variables)

1. () A quantity whose value is random and to which a probability distribution is assigned, such as the possible outcome of a roll of a dice.
2. (statistics, formally) A measurable function from a sample space to the measurable space of possible values of the variable.
• 1996, Ron C. Mittelhammer, Mathematical Statistics for Economics and Business, volume 78, Springer, page 45:
Henceforth the symbol $X(w)$ will be used for the random variable $X:S\rightarrow \mathbb {R}$ .
• 2009, Christian Perwass, Geometric Algebra with Applications in Engineering, Springer, page 351:
The particular example considered here is the Hilbert space of random variables.
• 2012, Scott Miller, Donald Childers, Probability and Random Processes, 2nd edition, Elsevier (Academic Press), page 177:
A two-dimensional random variable is a mapping of the points in the sample space to ordered pairs {x, y}. Usually, when dealing with a pair of random variables, the sample space naturally partitions itself so that it can be viewed as a combination of two simpler sample spaces.

#### Usage notes

Especially in discrete cases, a random variable is sometimes said to be indexed by the domain of its defining function, leading to notations such as $X[n]$ and $X_{i}$ to represent particular values of the codomain.