Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Joint and Marginal Distributions

Chapter 13 Probability & information

Chapter 13: Probability and Random Variables — Joint, Marginal, & Conditional Probabilities

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From the book

Chapter 13: Probability and Random Variables. In the chapter mind map this icon labels Joint, Marginal, & Conditional Probabilities. The discussion below is excerpted and lightly edited from § Definition: Discrete variables, marginal PMF in Mathematics for AI and Machine Learning.

For discrete random variables $X, Y$ with joint PMF $P(X=x, Y=y)$, the marginal PMF of $X$ is

What this drawing shows

What you see. Shows a joint distribution projected or summed into marginal distributions along each variable axis.

In the mind map. Chapter 13 — Joint, Marginal, & Conditional Probabilities. See From the book above for definitions, figures, and worked examples.

Where to read next

Open Chapter 13 companion →

Read the full definitions, figures, and worked examples in Chapter 13: Probability and Random Variables — see the mind-map node Joint, Marginal, & Conditional Probabilities.