Probability Mass Function

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ProbabilityStochasticProcessesInfoTheory

Definition

Let $X$ be a discrete random variable with range $\mathscr{X}=\{x_1,...\}$ . The pmf of $X$ is the function $p:\mathbb{R}\to\mathbb{R}$ defined by: $\begin{align*} p(x):=\ &P(X=x),\ &&x\in\mathscr{X}\\ p(x)=\ &0, \ &&x\notin\mathscr{X} \end{align*}$

Lemma

$p(x)\ge 0 \ \forall x\in\mathscr{X}$
$\sum_{x\in\mathscr{X}}p(x)=1$

Probability Mass Function

Definition

Lemma

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