Definition: Law of marginal probability
Index:
The Book of Statistical Proofs ▷
General Theorems ▷
Probability theory ▷
Probability ▷
Marginal probability
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Metadata: ID: D50 | shortcut: prob-marg | author: JoramSoch | date: 2020-05-10, 20:01.
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
\[\label{eq:prob-marg-cont} p(A) = \int_{\mathcal{X}} p(A,x) \, \mathrm{d}x \; .\]- Wikipedia (2020): "Marginal distribution"; in: Wikipedia, the free encyclopedia, retrieved on 2020-05-10; URL: https://en.wikipedia.org/wiki/Marginal_distribution#Definition.
- Jason Browlee (2019): "A Gentle Introduction to Joint, Marginal, and Conditional Probability"; in: Machine Learning Mastery, retrieved on 2021-08-01; URL: https://machinelearningmastery.com/joint-marginal-and-conditional-probability-for-machine-learning/.
Metadata: ID: D50 | shortcut: prob-marg | author: JoramSoch | date: 2020-05-10, 20:01.