Category:Definitions/Random Variables

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This category contains definitions related to Random Variables.
Related results can be found in Category:Random Variables.


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

Let $\struct {S, \Sigma'}$ be a measurable space.


A random variable on $\struct {\Omega, \Sigma, \Pr}$, taking values in $\struct {S, \Sigma'}$, is a $\Sigma \, / \, \Sigma'$-measurable mapping $X : \Omega \to S$.