Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Expectation

Chapter 13 Probability & information

Chapter 13: Probability and Random Variables — Expectation, Variance & Covariance

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From the book

Chapter 13: Probability and Random Variables. In the chapter mind map this icon labels Expectation, Variance & Covariance. The discussion below is excerpted and lightly edited from § Definition: Covariance in Mathematics for AI and Machine Learning.

For random variables $X \in \mathbb{R}$ and $Y \in \mathbb{R}$, the covariance is defined as

What this drawing shows

What you see. Represents averaging a random variable under a probability distribution, the central operation behind moments and risk.

In the mind map. Chapter 13 — Expectation, Variance & Covariance. 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 Expectation, Variance & Covariance.