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) $X$ and $Y$ are not independent (of each other).