Cumulative Distributions
Definition
Given a distribution $p: \Omega \to \R $, the
cumulative distribution (or
cumulative distribution
function, cdf) of a
random variable $x: \Omega \to \R $ is the
function $F: \R \to \R $ defined by
\[
F(t) = \mathbfsf{P} (x \leq t),
\]
Properties
The cumulative distribution of any random
variable is