# Category:Probability Density Functions

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This category contains results about **Probability Density Functions**.

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

Let $X$ be an absolutely continuous random variable on $\struct {\Omega, \Sigma, \Pr}$.

Let $P_X$ be the probability distribution of $X$.

Let $\map \BB \R$ be the Borel $\sigma$-algebra of $\R$.

Let $\lambda$ be the Lebesgue measure on $\struct {\R, \map \BB \R}$.

We define the **probability density function** $f_X$ by:

- $\ds f_X = \frac {\d P_X} {\d \lambda}$

where $\dfrac {\d P_X} {\d \lambda}$ denotes the Radon-Nikodym derivative of $P_X$ with respect to $\lambda$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Probability Density Functions"

The following 3 pages are in this category, out of 3 total.