random variable

English

Noun

random variable (plural random variables)

1. (statistics, broadly) 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.

Synonyms

• variate
• (broadly): random quantity
• (broadly, formally): aleatory variable, stochastic variable

Derived terms

• continuous random variable
• discrete random variable

Translations

measurable function from a sample space

• Arabic: مُتَغَيِّر عَشْوَائِيّ (mutaḡayyir ʕašwāʔiyy)
• Czech: náhodná veličina f
• Esperanto: stokasto
• Finnish: satunnaismuuttuja
• German: Zufallsvariable (de) f, Zufallsgröße f
• Greek: τυχαία μεταβλητή f (tychaía metavlití)
• Hebrew: משתנה מקרי (he) m (mishtané mikrí)
• Hungarian: valószínűségi változó (hu), valváltozó
• Icelandic: hending (is) f, slembibreyta f, slembistærð f, slemba f
• Japanese: 確率変数
• Maori: taurangi matapōkere
• Polish: zmienna losowa (pl) f
• Romanian: variabilă aleatorie f, variabilă incidentală f
• Spanish: variable aleatoria f
• Swedish: slumpvariabel c
• Tagalog: alisagang aligin
• Ukrainian: випадко́ва величина́ f (vypadkóva velyčyná)
• Welsh: hapnewidyn m