Index: The Book of Statistical ProofsGeneral Theorems ▷ Probability theory ▷ Probability functions ▷ Probability mass function

Definition: Let $X$ be a discrete random variable with possible outcomes $\mathcal{X}$. Then, $f_X(x): \mathbb{R} \to [0,1]$ is the probability mass function (PMF) of $X$, if

\[\label{eq:pmf-def-s0} f_X(x) = 0\]

for all $x \notin \mathcal{X}$,

\[\label{eq:pmf-def-s1} \mathrm{Pr}(X = x) = f_X(x)\]

for all $x \in \mathcal{X}$ and

\[\label{eq:pmf-def-s2} \sum_{x \in \mathcal{X}} f_X(x) = 1 \; .\]

Metadata: ID: D9 | shortcut: pmf | author: JoramSoch | date: 2020-02-13, 19:09.