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
3 - Distributions on the Real Line
from Part I - Elements of Probability Theory
Published online by Cambridge University Press: 22 July 2022
- 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
Measurements are often numerical in nature, which naturally leads to distributions on the real line. We start our discussion of such distributions in the present chapter, and in the process introduce the concept of random variable, which is really a device to facilitate the writing of probability statements and the derivation of the corresponding computations. We introduce objects such as the distribution function, survival function, and quantile function, any of which characterizes in the underlying distribution.
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- Chapter
- Information
- Principles of Statistical AnalysisLearning from Randomized Experiments, pp. 34 - 40Publisher: Cambridge University PressPrint publication year: 2022