2.12 The Law of Large Numbers
2.13 Law of Large Numbers and Frequentist Probability
References
3 Probability Density Functions
3.1 Introduction
3.2 Definition of Probability Density Function
3.3 Statistical Indicators in the Continuous Case
3.4 Cumulative Distribution
3.5 Continuous Transformations of Variables
3.6 Marginal Distributions
3.7 Uniform Distribution
3.8 Gaussian Distribution
3.9 [chi]2 Distribution
3.10 Log Normal Distribution
3.11 Exponential Distribution
3.12 Gamma Distribution
3.13 Beta Distribution
3.14 Breit-Wigner Distribution

Intro
Preface
Contents
List of Figures
List of Tables
List of Examples
1 Introduction to Probability and Inference
1.1 Why Probability Matters to a Physicist
1.2 Random Processes and Probability
1.3 Different Approaches to Probability
1.4 Classical Probability
1.5 Problems with the Generalization to the Continuum
1.6 The Bertrand's Paradox
1.7 Axiomatic Probability Definition
1.8 Conditional Probability
1.9 Independent Events
1.10 Law of Total Probability
1.11 Inference
1.12 Measurements and Their Uncertainties

1.13 Statistical and Systematic Uncertainties
1.14 Frequentist vs Bayesian Inference
References
2 Discrete Probability Distributions
2.1 Introduction
2.2 Joint and Marginal Probability Distributions
2.3 Conditional Distributions and Chain Rule
2.4 Independent Random Variables
2.5 Statistical Indicators: Average, Variance, and Covariance
2.6 Statistical Indicators for Finite Samples
2.7 Transformations of Variables
2.8 The Bernoulli Distribution
2.9 The Binomial Distribution
2.10 The Multinomial Distribution
2.11 The Poisson Distribution

3.15 Relativistic Breit-Wigner Distribution
3.16 Argus Distribution
3.17 Crystal Ball Function
3.18 Landau Distribution
3.19 Mixture of PDFs
3.20 Central Limit Theorem
3.21 Probability Distributions in Multiple Dimension
3.22 Independent Variables
3.23 Covariance, Correlation, and Independence
3.24 Conditional Distributions
3.25 Gaussian Distributions in Two or More Dimensions
References
4 Random Numbers and Monte Carlo Methods
4.1 Pseudorandom Numbers
4.2 Properties of Pseudorandom Generators
4.3 Uniform Random Number Generators

4.4 Inversion of the Cumulative Distribution
4.5 Random Numbers Following a Finite Discrete Distribution
4.6 Gaussian Generator Using the Central Limit Theorem
4.7 Gaussian Generator with the Box-Muller Method
4.8 Hit-or-Miss Monte Carlo
4.9 Importance Sampling
4.10 Numerical Integration with Monte Carlo Methods
4.11 Markov Chain Monte Carlo
References
5 Bayesian Probability and Inference
5.1 Introduction
5.2 Bayes' Theorem
5.3 Bayesian Probability Definition
5.4 Decomposing the Denominator in Bayes' Formula