Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Probability ▷ Marginal probability

Definition: (law of marginal probability, also called “sum rule”) Let $A$ and $X$ be two arbitrary statements about random variables, such as statements about the presence or absence of an event or about the value of a scalar, vector or matrix. Furthermore, assume a joint probability distribution $p(A,X)$. Then, $p(A)$ is called the marginal probability of $A$ and,

1) if $X$ is a discrete random variable with domain $\mathcal{X}$, is given by

\[\label{eq:prob-marg-disc} p(A) = \sum_{x \in \mathcal{X}} p(A,x) \; ;\]

2) if $X$ is a continuous random variable with domain $\mathcal{X}$, is given by

\[\label{eq:prob-marg-cont} p(A) = \int_{\mathcal{X}} p(A,x) \, \mathrm{d}x \; .\]
 
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Metadata: ID: D50 | shortcut: prob-marg | author: JoramSoch | date: 2020-05-10, 20:01.