# Definition:Probability Distribution

## Definition

 It has been suggested that this page or section be merged into Definition:Probability Mass Function. (Discuss)

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 $\tuple {\R, \map \BB \R}$, where $\map \BB \R$ denotes the Borel $\sigma$-algebra on $\R$.

## Also known as

The probability distribution of $X$ may also be called the distribution or law of $X$.

It is also known as the probability mass function.

## Also see

• Results about probability distributions can be found here.