Probability: a lively introduction

Tijms H. Probability: A Lively Introduction
Title
Contents
Preface
1 Foundations of Probability Theory
	1.1 Probabilistic Foundations
	1.2 Classical Probability Model
	1.3 Geometric Probability Model
	1.4 Compound Chance Experiments
	1.5 Some Basic Rules
	1.6 Inclusion–Exclusion Rule
2 Conditional Probability
	2.1 Concept of Conditional Probability
	2.2 Chain Rule for Conditional Probabilities
	2.3 Law of Conditional Probability
	2.4 Bayes’ Rule in Odds Form
	2.5 Bayesian Inference − Discrete Case
3 Discrete Random Variables
	3.1 Concept of a Random Variable
	3.2 Expected Value
	3.3 Expected Value of Sums of Random Variables
	3.4 Substitution Rule and Variance
	3.5 Independence of Random Variables
	3.6 Binomial Distribution
	3.7 Poisson Distribution
	3.8 Hypergeometric Distribution
	3.9 Other Discrete Distributions
4 Continuous Random Variables
	4.1 Concept of Probability Density
	4.2 Expected Value of a Continuous Random Variable
	4.3 Substitution Rule and the Variance
	4.4 Uniform and Triangular Distributions
	4.5 Exponential Distribution
	4.6 Gamma, Weibull, and Beta Distributions
	4.7 Normal Distribution
	4.8 Other Continuous Distributions
	4.9 Inverse-Transformation Method and Simulation
	4.10 Failure-Rate Function
	4.11 Probability Distributions and Entropy
5 Jointly Distributed Random Variables
	5.1 Joint Probability Mass Function
	5.2 Joint Probability Density Function
	5.3 Marginal Probability Densities
	5.4 Transformation of Random Variables
	5.5 Covariance and Correlation Coefficient
6 Multivariate Normal Distribution
	6.1 Bivariate Normal Distribution
	6.2 Multivariate Normal Distribution
	6.3 Multidimensional Central Limit Theorem
	6.4 Chi-Square Test
7 Conditioning by Random Variables
	7.1 Conditional Distributions
	7.2 Law of Conditional Probability for Random Variables
	7.3 Law of Conditional Expectation
	7.4 Conditional Expectation as a Computational Tool
	7.5 Bayesian Inference − Continuous Case
8 Generating Functions
	8.1 Generating Functions
	8.2 Branching Processes and Generating Functions
	8.3 Moment-Generating Functions
	8.4 Central Limit Theorem Revisited
9 Additional Topics in Probability
	9.1 Bounds and Inequalities
	9.2 Strong Law of Large Numbers
	9.3 Kelly Betting System
	9.4 Renewal–Reward Processes
10 Discrete-Time Markov Chains
	10.1 Markov Chain Model
	10.2 Time-Dependent Analysis of Markov Chains
	10.3 Absorbing Markov Chains
	10.4 Long-Run Analysis of Markov Chains
	10.5 Markov Chain Monte Carlo Simulation
11 Continuous-Time Markov Chains
	11.1 Markov Chain Model
	11.2 Time-Dependent Probabilities
	11.3 Limiting Probabilities
Appendix A: Counting Methods
Appendix B: Basics of Set Theory
Appendix C: Some Basic Results from Calculus
Appendix D: Basics of Monte Carlo Simulation
Answers to Odd-Numbered Problems
Index