A First Course in Probability, Global Edition

✍ Scribed by Sheldon M. Ross

• Publisher: Pearson
• Year: 2020
• Tongue: English
• Leaves: 530
• Edition: 10
• Category: Library

✦ Synopsis

For upper-level to graduate courses in Probability or Probability and Statistics, for majors in mathematics, statistics, engineering, and the sciences.

Explores both the mathematics and the many potential applications of probability theory

A First Course in Probability is an elementary introduction to the theory of probability for students 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 through numerous examples. The 10th Edition includes many new and updated problems, exercises, and text material chosen both for interest level and for use in building student intuition about probability.

0134753119 / 9780134753119 A First Course in Probability, 10/e

 

✦ Table of Contents

Front Cover
Title Page
Copyright Page
Contents
Preface
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 Independence
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
4.6.1 Properties of Binomial Random Variables
4.6.2 Computing the Binomial Distribution Function
4.7 The Poisson Random Variable
4.7.1 Computing the Poisson Distribution Function
4.8 Other Discrete Probability Distributions
4.8.1 The Geometric Random Variable
4.8.2 The Negative Binomial Random Variable
4.8.3 The Hypergeometric Random Variable
4.8.4 The Zeta (or Zipf) Distribution
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
5.4.1 The Normal Approximation to the Binomial Distribution
5.5 Exponential Random Variables
5.5.1 Hazard Rate Functions
5.6 Other Continuous Distributions
5.6.1 The Gamma Distribution
5.6.2 The Weibull Distribution
5.6.3 The Cauchy Distribution
5.6.4 The Beta Distribution
5.6.5 The Pareto Distribution
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
6.3.1 Identically Distributed Uniform Random Variables
6.3.2 Gamma Random Variables
6.3.3 Normal Random Variables
6.3.4 Poisson and Binomial 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
7.2.1 Obtaining Bounds from Expectations Via the Probabilistic Method
7.2.2 The Maximum–Minimums Identity
7.3 Moments of the Number of Events That Occur
7.4 Covariance, Variance of Sums, and Correlations
7.5 Conditional Expectation
7.5.1 Definitions
7.5.2 Computing Expectations by Conditioning
7.5.3 Computing Probabilities by Conditioning
7.5.4 Conditional Variance
7.6 Conditional Expectation and Prediction
7.7 Moment Generating Functions
7.7.1 Joint Moment Generating Functions
7.8 Additional Properties of Normal Random Variables
7.8.1 The Multivariate Normal Distribution
7.8.2 The Joint Distribution of the Sample Mean and Sample Variance
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 ofIndependent Bernoulli Random Variables by a Poisson RandomVariable
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
10.2.1 The Inverse Transformation Method
10.2.2 The Rejection Method
10.3 Simulating from Discrete Distributions
10.4 Variance Reduction Techniques
10.4.1 Use of Antithetic Variables
10.4.1 Use of Antithetic Variables
10.4.2 Variance Reduction by Conditioning
10.4.3 Control Variates
Summary
Problems
Self-Test Problems and Exercises
Answers to Selected Problems
Solutions to Self-Test Problems
and Exercises
Index
Back Cover