First Course in Probability, A, 10th edition

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
• Summary
• Problems
• Theoretical Exercises
• Self-Test Problems and Exercises

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
• Summary
• Problems
• Theoretical Exercises
• Self-Test Problems and Exercises

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
• Summary
• Problems
• Theoretical Exercises
• Self-Test Problems and Exercises

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
• Summary
• Problems
• Theoretical Exercises
• Self-Test Problems and Exercises

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
• 5.6 Other Continuous Distributions
• 5.7 The Distribution of a Function of a Random Variable
• Summary
• Problems
• Theoretical Exercises
• Self-Test Problems and Exercises

6. Jointly Distributed Random Variables

• 6.1 Joint Distribution Functions
• 6.2 Independent Random Variables
• 6.3 Sums of Independent Random Variables
• 6.4 Conditional Distributions: Discrete Case
• 6.5 Conditional Distributions: Continuous Case
• 6.6 Order Statistics
• 6.7 Joint Probability Distribution of Functions of Random Variables
• 6.8 Exchangeable Random Variables
• Summary
• Problems
• Theoretical Exercises
• Self-Test Problems and Exercises

7. Properties of Expectation

• 7.1 Introduction
• 7.2 Expectation of Sums of Random Variables
• 7.3 Moments of the Number of Events that Occur
• 7.4 Covariance, Variance of Sums, and Correlations
• 7.5 Conditional Expectation
• 7.6 Conditional Expectation and Prediction
• 7.7 Moment Generating Functions
• 7.8 Additional Properties of Normal Random Variables
• 7.9 General Definition of Expectation
• Summary
• Problems
• Theoretical Exercises
• Self-Test Problems and Exercises

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
• Summary
• Problems
• Theoretical Exercises
• Self-Test Problems and Exercises

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
• Summary
• Problems and Theoretical Exercises
• Self-Test Problems and Exercises

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
• Summary
• Problems
• Self-Test Problems and Exercises

Answers to Selected Problems

Solutions to Self-Test Problems and Exercises

Index

Common Discrete Distributions

Common Continuous Distributions