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(x_k) is the probability of the variable x having the value x_k.

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

• <math>p(x_{k}) \geq 0; \forall x </math>
• <math>\sum_{k} p(x_{k}) = 1 </math>

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