Probability mass function
Backlinks: Experiments in probability theory
Probability mass function
Source: Wiki
Each outcome $\omega$ in the
sample space
$\Omega$ is assigned a probability value via the probability mass function $p(\omega)$ with the properties
$$
\begin{align}
p(\omega) &\in \left[ 0, 1\right] \quad \forall, \omega \in \Omega\
\sum_{\omega \in \Omega} p(\omega) &= 1
\end{align}
$$
Source: Yang
$X$ is distributed according to the distribution $P$, $$X \sim P(x) ~.$$
For a specific instance of $X$ (or outcome), evaluating the pmf gives the probability $$P(X = x_i) = P(x_i) = p_i \geq 0$$