law of a random variable

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

In particular, the law of $X$ is the pushforward of $\mu$ along $X$.

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

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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.