nLab
law of a random variable

Contents

Contents

Idea

Given a probability space (S,μ)(S,\mu) and a random variable X:SX \colon S \to \mathbb{R} with values in the real numbers, the law of XX is the probability measure on \mathbb{R} which to a measurable subset assigns the probability that XX takes values in this subset.

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

Examples

Example

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

References

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Last revised on July 21, 2021 at 03:56:46. See the history of this page for a list of all contributions to it.