Definition:Independent Random Variables/Dependent

Definition

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 dependent (on each other) if and only if $X$ and $Y$ are not independent (of each other).

Sources

• 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $\S 3.3$: Independence of discrete random variables