nLab law of a random variable




Given a probability space (S,,μ)(S,\mathcal{F},\mu) and a random variable or random element f:SXf \colon S \to X, the law or distribution of ff (or sometimes, of XX) is the probability measure on XX which to a measurable subset AXA\subseteq X assigns the probability that ff takes values in AA.

In particular, the law of ff is the pushforward of μ\mu along ff.



The law of a deterministic random variable is a Dirac measure.

See also

category: probability

Last revised on February 20, 2024 at 17:43:27. See the history of this page for a list of all contributions to it.