Definition:Probability Density Function of Bivariate Distribution/Continuous

Definition

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

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

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

$\ds \map p {x, y} := \int_{-\infty}^x \int_{-\infty}^y \map f {s, t} \rd t \rd s$

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Also known as

Probability density function is often conveniently abbreviated as p.d.f. or pdf.

Sometimes it is also referred to as the density function.

It is also known as a frequency function, which is also used for probability mass function

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