Definition:Independent Random Variables/Dependent

Definition
Let $\mathcal E$ be an experiment with probability space $\left({\Omega, \Sigma, \Pr}\right)$. Let $X$ and $Y$ be random variables on $\left({\Omega, \Sigma, \Pr}\right)$.

Then $X$ and $Y$ are defined as dependent (on each other) $X$ and $Y$ are not independent (of each other).