# Category:Definitions/Probability Distributions

This category contains definitions related to Probability Distributions.
Related results can be found in Category:Probability Distributions.

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

Let $X: \Omega \to \R$ be a random variable on $\tuple {\Omega, \Sigma, \Pr}$.

Then the probability distribution of $X$ is the pushforward $X_* \Pr$ of $\Pr$ on $\tuple {\R, \mathcal B \paren {\R} }$, where $\mathcal B \paren {\R}$ denotes the Borel $\sigma$-algebra on $\R$.

## Pages in category "Definitions/Probability Distributions"

The following 23 pages are in this category, out of 23 total.