Book contents
- Frontmatter
- Contents
- Preface
- Guide for Instructors
- 1 Introduction to Probability
- 2 Probability Distributions
- 3 Law of Large Numbers and Central Limit Theorem
- 4 Large Deviations
- 5 Statistical Inference and Experimental Data Analysis
- 6 Multivariate and Correlated Experimental Data
- 7 Random Walkers
- 8 Generating Functions and Chain Reactions
- 9 Recurrent Events
- 10 Markov Chains
- 11 Numerical Simulations
- 12 Correlated Events
- 13 Continuous-Time Markov Processes
- 14 Entropy, Probability, and Statistical Mechanics
- References
- Index
1 - Introduction to Probability
Published online by Cambridge University Press: 24 July 2025
Book contents
- Frontmatter
- Contents
- Preface
- Guide for Instructors
- 1 Introduction to Probability
- 2 Probability Distributions
- 3 Law of Large Numbers and Central Limit Theorem
- 4 Large Deviations
- 5 Statistical Inference and Experimental Data Analysis
- 6 Multivariate and Correlated Experimental Data
- 7 Random Walkers
- 8 Generating Functions and Chain Reactions
- 9 Recurrent Events
- 10 Markov Chains
- 11 Numerical Simulations
- 12 Correlated Events
- 13 Continuous-Time Markov Processes
- 14 Entropy, Probability, and Statistical Mechanics
- References
- Index
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Summary
The foundations of modern probability theory are briefly presented and discussed for both discrete and continuous stochastic variables. Without daring to give a rigorous mathematical construction – but citing different extremely well-written handbooks on the matter – the axiomatic theory of Kolmogorov and the concepts of joint, conditional, and marginal probability are introduced, along with the operations of union and intersection of generic random events. Eventually, Bayes’ formula is put forward with some examples. This will be at the cornerstone of statistical inference methods reported in Chapters 5 and 6.
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- Probability Theory for Quantitative Scientists , pp. 1 - 22Publisher: Cambridge University PressPrint publication year: 2025
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