probability mass function

A probability mass function is a probability distribution which maps every value of a discrete random variable to its associated probability.

Formally,
a discrete random variable $X:\mathrm{\Omega }\to \mathbb{R}$ has a probability mass function $p:\mathbb{R}\to [0,1]$ such that

i.e. $p(x)$ is the probability that $X$ takes a value of exactly $x$.