Definition:Joint Cumulative Distribution Function/Discrete

Definition

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

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

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

$\ds \map {F_{X, Y} } {x, y} := \sum_{x_i \mathop \le x} \sum_{y_j \mathop \le y} \map {p_{i j} } {x, y}$

where $p_{i j}$ denotes the probability density function.

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