Definition:Probability Mass Function/General Definition

Definition
Let $X = \left\{{X_1, X_2, \ldots, X_n}\right\}$ be a set of discrete random variables on $\left({\Omega, \Sigma, \Pr}\right)$.

Then the joint (probability) mass function of $X$ is (real-valued) function $p_X: \R^n \to \left[{0 \,.\,.\, 1}\right]$ defined as:
 * $\forall x = \left({x_1, x_2, \ldots, x_n}\right) \in \R^n: p_X \left({x}\right) = \Pr \left({X_1 = x_1, X_2 = x_2, \ldots, X_n = x_n}\right)$

The properties of the two-element case can be appropriately applied.