Category:Definitions/Joint Cumulative Distribution Functions

This category contains definitions related to Joint Cumulative Distribution Functions.
Related results can be found in Category:Joint Cumulative Distribution Functions.

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $X$ and $Y$ be real-valued random variables on $\struct {\Omega, \Sigma, \Pr}$.

The joint cumulative distribution function of $X$ and $Y$ is defined and denoted as:

$\forall x, y \in \R: \map {F_{X, Y} } {x, y} := \map \Pr {X \le x, Y \le y}$