\begin{definition}[Definition:Independent Random Variables/Discrete/General Definition/Definition 2]
Let $\EE$ be an experiment with probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $X = \tuple {X_1, X_1, \ldots, X_n}$ be an ordered tuple of random variables.
$X$ is '''independent''' {{iff}}:
:$\ds \map {p_X} x = \prod_{k \mathop = 1}^n \map {p_{X_k} } {x^k}$
for all $x = \tuple {x_1, x_2, \ldots, x_n} \in \R^n$.
\end{definition}