Definition:Probability Density Function of Bivariate Distribution

Definition

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

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

The probability density function of $X$ and $Y$ is defined and denoted as:

$\map {p_{i j} } {x, y} := \map \Pr {X = x_i, Y = y_j}$

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