Cover -- Table of Contents -- Acknowledgments -- About the Author -- Introduction -- Chapter 1: Overview -- How to Use This Book -- Chapter 2: Introduction to Probability and Its Applications -- Chapter 3: Set Theory -- Chapter 4: Counting Techniques -- Chapter 5: Computing Probabilities -- Chapter 6: Conditional Probability and Independence -- Chapter 7: Discrete Random Variables -- Chapter 8: Continuous Random Variables -- Chapter 9: The Normal Distribution -- Chapter 10: Expected Value -- Chapter 11: Laws of Large Numbers -- Chapter 12: Markov Chains -- Chapter 13: The Axioms of Probability -- Chapter 2: Introduction to Probability and Its Applications -- 2.1 Probability -- 2.2 Ways to Measure Probability -- 2.3 Empirical Probability and Subjective Probability -- 2.4 How Probability Is Applied -- 2.5 Weather -- Chapter 2 Summary -- Chapter 2 Practice Problems -- Answers to Chapter 2 Practice Problems -- Chapter 3: Set Theory -- 3.1 Sets -- 3.2 Venn Diagrams -- 3.3 Subsets -- 3.4 Sample Spaces and Events -- 3.5 Some Special Sets -- 3.6 Operations with Sets -- 3.7 Properties of Set Operations -- Chapter 3 Summary -- Properties of Set Operations -- Chapter 3 Practice Problems -- Answers to Chapter 3 Practice Problems -- Chapter 4: Counting Techniques -- 4.1 Counting Principles -- Product Rule for Counting -- Sum Rule for Counting -- 4.2 Permutations -- 4.3 Combinations -- 4.4 Partitions -- 4.5 Challenging Counting Problems -- 4.6 Binomial Coefficients -- 4.7 Pascal's Triangle -- Chapter 4 Summary -- Chapter 4 Practice Problems -- Answers to Chapter 4 Practice Problems -- Chapter 5: Computing Probabilities -- 5.1 About Numerical Computations -- 5.2 General Principles for Computing Probabilities -- Counting Events -- Multiplication Rule for Probability -- Complement Rule for Probability -- Addition Rule of Probability for Mutually Exclusive Events.

General Addition Rule for Probability -- Inequality for Probabilities -- Bonferroni's Inequality -- 5.3 Problems Using Dice -- 5.4 Problems Involving Coin Tossing -- 5.5 Problems Involving Cards -- 5.6 Geometric Probability -- 5.7 Quality Control -- 5.8 Birthday Problems -- 5.9 Transmission Errors -- Chapter 5 Summary -- Chapter 5 Practice Problems -- Dice Problems -- Coin Problems -- Card Problems -- Quality Control Problems -- Birthday Problems -- Geometric Probability Problems -- Transmission Error Problems -- More Challenging Problems -- Answers to Chapter 5 Practice Problems -- Chapter 6: Conditional Probability and Independence -- 6.1 Conditional Probability -- 6.2 Multiplication Theorem for Conditional Probability -- 6.3 Switching Conditions -- 6.4 Partitions and the Law of Total Probability -- 6.5 Bayes' Formula for Conditional Probability -- 6.6 Independent Events -- Chapter 6 Summary -- Chapter 6 Practice Problems -- Conditional Probability -- Bayes' Formula -- Independent Events -- Answers to Chapter 6 Practice Problems -- Chapter 7: Discrete Random Variables -- 7.1 Random Variables -- 7.2 Probability Frequency Function -- 7.3 Cumulative Distribution Function of a Random Variable -- 7.4 Joint Distribution of Two Random Variables -- 7.5 The Bernoulli Random Variable and the Binomial Distribution -- 7.6 The Poisson Distribution -- 7.7 The Geometric Distribution -- 7.8 The Negative Binomial Distribution -- 7.9 The Hypergeometric Distribution -- 7.10 The Multinomial Distribution -- Chapter 7 Summary -- Chapter 7 Practice Problems -- Answers to Chapter 7 Practice Problems -- Chapter 8: Continuous Random Variables -- 8.1 Continuous Random Variables -- 8.2 Cumulative Distribution Function of a Continuous Random Variable -- 8.3 The Uniform Distribution -- 8.4 The Normal Distribution -- 8.5 The Exponential Distribution -- Chapter 8 Summary.

Chapter 8 Practice Problems -- Answers to Chapter 8 Practice Problems -- Chapter 9: The Normal Distribution -- 9.1 Properties of the Normal Distribution -- 9.2 Computing Probabilities for the Standard Normal Distribution -- Summary for Computing Probabilities for the Standard Normal Distribution -- 9.3 Computing Probabilities for Any Normal Distribution -- Linear Interpolation -- 9.4 The Normal Approximation of the Binomial Distribution -- Chapter 9 Summary -- Chapter 9 Practice Problems -- Answers to Chapter 9 Practice Problems -- Chapter 10: Expected Value -- 10.1 Expected Value -- 10.2 Expected Value for Discrete Random Variables -- Coin Toss -- Cards -- Lottery -- Bernoulli Trial -- Binomial Experiment -- Poisson Distribution -- Geometric Distribution -- Negative Binomial Distribution -- Hypergeometric Distribution -- 10.3 Expected Value for Continuous Random Variables -- Uniform Distribution -- Normal Distribution -- Exponential Distribution -- 10.4 Expectation of a Multiple or Sum of Random Variables -- 10.5 Conditional Expectation -- Chapter 10 Summary -- Chapter 10 Practice Problems -- Answers to Chapter 10 Practice Problems -- Chapter 11: Laws of Large Numbers -- 11.1 Describing a Probability Distribution -- 11.2 The Chebyshev Inequality -- 11.3 The Weak Law of Large Numbers -- 11.4 The Central Limit Theorem -- 11.5 The Strong Law of Large Numbers -- 11.6 Comparison of Inequalities and Laws -- Chapter 11 Summary -- Chapter 11 Practice Problems -- Answers to Chapter 11 Practice Problems -- Chapter 12: Markov Chains -- 12.1 Examples of Markov Chains -- The Random Walk -- Demographics -- Definition of a Markov Chain -- 12.2 Vectors -- 12.3 Matrices -- Properties of Matrix Multiplication -- 12.4 Long-Term Behavior of Markov Chains -- Steady States -- Periodic States -- Chapter 12 Summary -- Chapter 12 Practice Problems.

Answers to Chapter 12 Practice Problems -- Chapter 13: The Axioms of Probability -- 13.1 The Axiomatic Structure of Mathematics -- 13.2 The Axioms of Probability -- 13.3 Theorems Derived from the Axioms of Probability -- 13.4 Probability Theory -- Chapter 13 Summary -- Chapter 13 Practice Problems -- Answers to Chapter 13 Practice Problems -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Z.