![[A First Course in Probability.png]] ## 1. Combinatorial Analysis 1.1 Introduction 1.2 The Basic Principle of Counting 1.3 Permutations 1.4 Combinations 1.5 Multinomial Coefficients 1.6 The Number of Integer Solutions of Equations ## 2. Axioms of Probability 2.1 Introduction 2.2 Sample Space and Events 2.3 Axioms of Probability 2.4 Some Simple Propositions 2.5 Sample Spaces Having Equally Likely Outcomes 2.6 Probability as a Continuous Set Function 2.7 Probability as a Measure of Belief ## 3. Conditional Probability and Inference 3.1 Introduction 3.2 Conditional Probabilities 3.3 Bayes’s Formula 3.4 Independent Events 3.5 P(·|F) Is a Probability ## 4. Random Variables 4.1 Random Variables 4.2 Discrete Random Variables 4.3 Expected Value 4.4 Expectation of a Function of a Random Variable 4.5 Variance 4.6 The Bernoulli and Binomial Random Variables 4.7 The Poisson Random Variable 4.8 Other Discrete Probability Distributions 4.9 Expected Value of Sums of Random Variables 4.10 Properties of the Cumulative Distribution Function --- ## 5. Continuous Random Variables 5.1 Introduction 5.2 Expectation and Variance of Continuous Random Variables 5.3 The Uniform Random Variable 5.4 Normal Random Variables 5.5 Exponential Random Variables 7.9 General Definition of Expectation > ⚠️ Note: Sections beyond 5.5 are renumbered from later chapters and included here in the publisher’s online contents (e.g., Section 7.9). --- ## 8. Limit Theorems 8.1 Introduction 8.2 Chebyshev’s Inequality and the Weak Law of Large Numbers 8.3 The Central Limit Theorem 8.4 The Strong Law of Large Numbers 8.5 Other Inequalities and a Poisson Limit Result 8.6 Bounding the Error Probability When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson Random Variable 8.7 The Lorenz Curve ## 9. Additional Topics in Probability 9.1 The Poisson Process 9.2 Markov Chains 9.3 Surprise, Uncertainty, and Entropy 9.4 Coding Theory and Entropy ## 10. Simulation 10.1 Introduction 10.2 General Techniques for Simulating Continuous Random Variables 10.3 Simulating from Discrete Distributions 10.4 Variance Reduction Techniques