Book contents
- Frontmatter
- Dedication
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Part I Elements of Probability Theory
- 1 Axioms of Probability Theory
- 2 Discrete Probability Spaces
- 3 Distributions on the Real Line
- 4 Discrete Distributions
- 5 Continuous Distributions
- 6 Multivariate Distributions
- 7 Expectation and Concentration
- 8 Convergence of Random Variables
- 9 Stochastic Processes
- Part II Practical Considerations
- Part III Elements of Statistical Inference
- References
- Index
7 - Expectation and Concentration
from Part I - Elements of Probability Theory
Published online by Cambridge University Press: 22 July 2022
Book contents
- Frontmatter
- Dedication
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Part I Elements of Probability Theory
- 1 Axioms of Probability Theory
- 2 Discrete Probability Spaces
- 3 Distributions on the Real Line
- 4 Discrete Distributions
- 5 Continuous Distributions
- 6 Multivariate Distributions
- 7 Expectation and Concentration
- 8 Convergence of Random Variables
- 9 Stochastic Processes
- Part II Practical Considerations
- Part III Elements of Statistical Inference
- References
- Index
Summary
An expectation is simply a weighted mean, and means are at the core of Probability Theory and Statistics. In Statistics, in particular, such expectations are used to define parameters of interest. It turns out that an expectation can be approximated by an empirical average based on a sample from the distribution of interest, and the accuracy of this approximation can be quantified via what is referred to as concentration inequalities.
- Type
- Chapter
- Information
- Principles of Statistical AnalysisLearning from Randomized Experiments, pp. 78 - 99Publisher: Cambridge University PressPrint publication year: 2022