There are two main concepts associated with a stochastic variable. The domain is the set $\mathbb D = \{x\}$ of all accessible values the variable can assume, so that $X \in \mathbb D$. An example of a discrete domain is the set of six different numbers that we may get by throwing of a dice, $x\in\{1,\,2,\,3,\,4,\,5,\,6\}$.

The probability distribution function (PDF) is a function $p(x)$ on the domain which, in the discrete case, gives us the probability or relative frequency with which these values of $X$ occur $$\begin{equation*} p(x) = \mathrm{Prob}(X=x). \end{equation*}$$