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 $$ \begin{equation*} p(x) = \mathrm{Prob}(X=x). \end{equation*} $$