# First Course in Probability, A, 10th edition

• Sheldon Ross

• Search, highlight, notes, and more
• Easily create flashcards
• Use the app for access anywhere
• 14-day refund guarantee

\$10.99per month

Minimum 4-month term, pay monthly or pay \$43.96 upfront

• Find it fast

Quickly navigate your eTextbook with search

• Stay organized

Access all your eTextbooks in one place

• Easily continue access

Keep learning with auto-renew

## Overview

A First Course in Probability explores the mathematics and potential applications of probability theory. It is an elementary introduction to the theory of probability for upper-level and graduate 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; new material on topics including the Pareto distribution, Poisson limit results, and the Lorenz curve; new examples such as computing NCAA basketball tournament win probabilities and the friendship paradox; revised and streamlined exposition for clarity and deeper understanding; and much more.

ISBN-13: 9780138027889

Category: Probability & Statistics

## Overview

### 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

#### Common Continuous Distributions

Pearson+ is your 1-stop shop with eTextbooks, study tools and exam prep features designed to help students get better grades in college. eTextbooks come with built-in tools that simplify studying, like flashcards, audiobook and search. Pearson+ also features Channels, which includes practice problems, study guides, Q&A with experts, video lessons that help you understand tricky topics and more—all in one place. Channels can be purchased separately or added on to your eTextbook at the time of purchase as part of the Study & Exam Prep Pack.
The Study & Exam Prep Pack includes practice problems, study guides, Q&A with experts, Channels video lessons that help you understand tricky topics and more. It can be added on to your eTextbook or your MyLab and Mastering learning platform at the time of purchase.
Your eTextbook subscription gives you access for 4 months. You can make a one‑time payment for the initial 4‑month term or pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 4‑month term ends. You can turn on auto‑renew in My account at any time to continue your subscription before your 4‑month term ends.

When you purchase an eTextbook subscription, it will last 4 months. You can renew your subscription by selecting Extend subscription on the Manage subscription page in My account before your initial term ends.

If you extend your subscription, we'll automatically charge you every month. If you made a one‑time payment for your initial 4‑month term, you'll now pay monthly. To make sure your learning is uninterrupted, please check your card details.

To avoid the next payment charge, select Cancel subscription on the Manage subscription page in My account before the renewal date. You can subscribe again in the future by purchasing another eTextbook subscription.

Channels is a video platform with thousands of explanations, solutions and practice problems to help you do homework and prep for exams. Videos are personalized to your course, and tutors walk you through solutions. Plus, interactive AI‑powered summaries and a social community help you better understand lessons from class.