Category:Definitions/Independent Random Variables

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

Let $\EE$ be an experiment with probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $X$ and $Y$ be random variables on $\struct {\Omega, \Sigma, \Pr}$.

Then $X$ and $Y$ are defined as independent (of each other) if and only if:

$\map \Pr {X = x, Y = y} = \map \Pr {X = x} \map \Pr {Y = y}$

where $\map \Pr {X = x, Y = y}$ is the joint probability mass function of $X$ and $Y$.