Definition:Probability Mass Function/General Definition

Definition

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

Then the joint (probability) mass function of $X$ is (real-valued) function $p_X: \R^n \to \closedint 0 1$ defined as:

$\forall x = \tuple {x_1, x_2, \ldots, x_n} \in \R^n: \map {p_X} x = \map \Pr {X_1 = x_1, X_2 = x_2, \ldots, X_n = x_n}$

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