Definition:Independent Random Variables

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 independent (of each other) iff:
 * $$\Pr \left({X = x \and Y = y}\right) = \Pr \left({X = x}\right) \Pr \left({Y = y}\right)$$