Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Independence

Chapter 13 Probability & information

Chapter 13: Probability and Random Variables — Independence & Conditional Independence

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Independence — high-resolution mind-map icon

From the book

Chapter 13: Probability and Random Variables. In the chapter mind map this icon labels Independence & Conditional Independence. The discussion below is excerpted and lightly edited from § Definition: Independence (Discrete) in Mathematics for AI and Machine Learning.

Discrete random variables $X$ and $Y$ are independent if

What this drawing shows

What you see. Represents variables whose joint distribution factorizes into separate marginals, indicating no statistical dependence.

In the mind map. Chapter 13 — Independence & Conditional Independence. 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 Independence & Conditional Independence.