Definition:Joint Cumulative Distribution Function

Definition

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:

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

Also see

• Results about joint cumulative distribution functions can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): bivariate distribution
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): distribution function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): bivariate distribution
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): distribution function