Category:Definitions/Probability Distributions

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