Probability Density Function

probability-theory

Definition

Probability Density Function

A probability density function $f$ is a point-wise function for continuous spaces that assigns a density to each outcome. This density represents the relative likelihood of the outcome. To obtain a probability, one must integrate the function over an interval.

$$f:\Omega \to [0,\infty )\subset \mathbb{R}$$

The analogue for discrete spaces is the probability mass function.

Note that the density is not a probability as the density can take values bigger than $1$.