Random variables

Assume that a probability space $ (S,{\cal F},P)$ is given. A random variable9.1 $ X$ is a function that maps $ S$ into $ {\mathbb{R}}$. Thus, $ X$ assigns a real value to every element of the sample space. This enables statistics to be conveniently computed over a probability space. If $ S$ is already a subset of $ {\mathbb{R}}$, $ X$ may by default represent the identity function.

Steven M LaValle 2012-04-20