## Definition A ==Probability Mass Function (PMF)== gives the probability that a discrete random variable $X$ equals a specific value $x$: $ p(x) = P(X = x) $ It must satisfy $p(x) \geq 0$ for all $x$ and $\sum_{\text{all } x} p(x) = 1$. > [!example]- A fair die is rolled. What is the PMF of the outcome $X$? > Each face is equally likely, so the PMF is: > $ p(x) = \frac{1}{6}, \quad x \in \{1, 2, 3, 4, 5, 6\} $ > We can verify: $\sum_{x=1}^{6} \frac{1}{6} = 1$. ✓