# First Course in Probability, A,10th edition

• Sheldon Ross University of Southern California

## eTextbook

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## MyLab

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For upper-level to graduate courses in Probability or Probability and Statistics.

### Explores the mathematics and potential applications of probability theory

A First Course in Probability is an elementary introduction to the theory of probability for students majoring in mathematics, statistics, engineering and the sciences. Through clear and intuitive explanations, it presents not only the mathematics of probability theory but also the many diverse possible applications of this subject using numerous examples. The 10th Edition includes many new and updated problems, exercises and text material chosen both for inherent interest and for use in building student intuition about probability.

### Hallmark features of this title

• Analysis is unique to the text and elegantly designed. Examples include the knockout tournament and multiple players gambling ruin problem, along with results concerning the sum of uniform and the sum of geometric random variables.
• Intuitive explanations are supported with an abundance of examples to give readers a thorough introduction to both the theory and applications of probability.
• 3 sets of exercises are given at the end of each chapter: Problems, Theoretical Exercises and Self-Test Problems and Exercises.
• Self-Test Problems and Exercises include complete solutions in the appendix, allowing students to test their comprehension and study for exams.

### New and updated features of this title

• New Examples throughout include Example 4n of Chapter 3 (computing NCAA basketball tournament win probabilities) and Example 5b of Chapter 4 (introducing the friendship paradox).
• Many new and updated problems are provided throughout.
• New material is provided on topics including the Pareto distribution (introduced in Section 5.6.5), Poisson limit results (Section 8.5), and the Lorenz curve (Section 8.7).
• Revised and streamlined exposition focuses on clarity and deeper understanding.

### Features of MyLab Statistics for the 10th Edition

• Exercises with immediate feedback: Over 2800 exercises reflect the approach and learning style of the text, and regenerate algorithmically to provide unlimited opportunity for practice and mastery. Theoretical Exercises (TE) and Self-Test Problems (ST) are included; most exercises offer learning aids such as guided solutions and sample problems, and provide helpful feedback on incorrect answers.
• Personalized homework: Students take a quiz or test and receive a personalized homework assignment based on their performance. In this way, they can focus on just the topics they have not yet mastered.
• StatCrunch® is Integrated directly into MyLab Statistics. This powerful web-based statistical software allows users to perform complex analyses, share data sets and generate compelling reports of their data.
• The vibrant online community offers tens of thousands shared data sets for students to analyze.StatCrunch can be accessed on a laptop, smartphone, or tablet when students visit the StatCrunch website from their device's browser.
• Performance Analytics enable instructors to see and analyze student performance across multiple courses. Based on their current course progress, a student's performance is identified above, at or below expectations through a variety of graphs and visualizations.
• Accessibility: Pearson works continuously to ensure our products are as accessible as possible to all students. Currently we work toward achieving WCAG 2.0 AA for our existing products (2.1 AA for future products) and Section 508 standards.

### 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