Probability Mass Function (PMF)

Definition

The probability mass function of a discrete random variable $X$ is

$$ p(x) = \mathbb{P}(X = x). $$

Requirements

  1. $p(x) \geq 0$ for all $x$.
  2. $\displaystyle\sum_{x} p(x) = 1$.

Unlike a PDF, a PMF gives actual probabilities: $p(x) \in [0, 1]$.