# Probability mass function

In probability theory, a probability mass function (p(x)) is a real-valued function of a discrete variable (x), such that the value p(xk) is the probability of the variable x having the value xk.

In order to qualify, such a function must meet the following criteria:

• $p(x_{k}) \geq 0; \forall x$
•  ∑ p(xk) = 1 k

The collection of pairs ( xk , p(xk) ) is the discrete probability distribution of x.