Fundamentals of Probability: With Stochastic Processes, 4th Edition (Hardback) book cover

Fundamentals of Probability

With Stochastic Processes, 4th Edition

By Saeed Ghahramani

Chapman and Hall/CRC

632 pages | 200 B/W Illus.

Companion Website
Purchasing Options:$ = USD
Hardback: 9781498755092
pub: 2018-09-04
$119.95
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Description

"The 4th edition of Ghahramani's book is replete with intriguing historical notes, insightful comments, and well-selected examples/exercises that, together, capture much of the essence of probability. Along with its Companion Website, the book is suitable as a primary resource for a first course in probability. Moreover, it has sufficient material for a sequel course introducing stochastic processes and stochastic simulation."

--Nawaf Bou-Rabee, Associate Professor of Mathematics, Rutgers University Camden, USA

"This book is an excellent primer on probability, with an incisive exposition to stochastic processes included as well. The flow of the text aids its readability, and the book is indeed a treasure trove of set and solved problems. Every sub-topic within a chapter is supplemented by a comprehensive list of exercises, accompanied frequently by self-quizzes, while each chapter ends with a useful summary and another rich collection of review problems."

--Dalia Chakrabarty, Department of Mathematical Sciences, Loughborough University, UK

"This textbook provides a thorough and rigorous treatment of fundamental probability, including both discrete and continuous cases. The book’s ample collection of exercises gives instructors and students a great deal of practice and tools to sharpen their understanding. Because the definitions, theorems, and examples are clearly labeled and easy to find, this book is not only a great course accompaniment, but an invaluable reference."

--Joshua Stangle, Assistant Professor of Mathematics, University of Wisconsin – Superior, USA

This one- or two-term calculus-based basic probability text is written for majors in mathematics, physical sciences, engineering, statistics, actuarial science, business and finance, operations research, and computer science. It presents probability in a natural way: through interesting and instructive examples and exercises that motivate the theory, definitions, theorems, and methodology. This book is mathematically rigorous and, at the same time, closely matches the historical development of probability. Whenever appropriate, historical remarks are included, and the 2096 examples and exercises have been carefully designed to arouse curiosity and hence encourage students to delve into the theory with enthusiasm.

New to the Fourth Edition:

  • 538 new examples and exercises have been added, almost all of which are of applied nature in realistic contexts
  • Self-quizzes at the end of each section and self-tests at the end of each chapter allow students to check their comprehension of the material
  • An all-new Companion Website includes additional examples, complementary topics not covered in the previous editions, and applications for more in-depth studies, as well as a test bank and figure slides. It also includes complete solutions to all self-test and self-quiz problems 

Saeed Ghahramani is Professor of Mathematics and Dean of the College of Arts and Sciences at Western New England University. He received his Ph.D. from the University of California at Berkeley in Mathematics and is a recipient of teaching awards from Johns Hopkins University and Towson University. His research focuses on applied probability, stochastic processes, and queuing theory.

Reviews

"This textbook provides a thorough and rigorous treatment of fundamental probability, including both discrete and continuous cases. The book’s ample collection of exercises gives instructors and students a great deal of practice and tools to sharpen their understanding. Because the definitions, theorems, and examples are clearly labeled and easy to find, this book is not only a great course accompaniment, but an invaluable reference."

~Joshua Stangle, University of Wisconsin

Table of Contents

  1. Axioms of Probability
  2. Introduction

    Sample Space and Events

    Axioms of Probability

    Basic Theorems

    Continuity of Probability Function

    Probabilities and Random Selection of Points from Intervals

    What Is Simulation?

    Chapter Summary

    Review Problems

    Self-Test on Chapter

  3. Combinatorial Methods
  4. Introduction

    Counting Principle

    Number of Subsets of a Set

    Tree Diagrams

    Permutations

    Combinations

    Stirling’s Formula

    Chapter Summary

    Review Problems

    Self-Test on Chapter

  5. Conditional Probability and Independence
  6. Conditional Probability

    Reduction of Sample Space

    The Multiplication Rule

    Law of Total Probability

    Bayes’ Formula

    Independence

    Chapter Summary

    Review Problems

    Self-Test on Chapter

  7. Distribution Functions and Discrete Random Variables
  8. Random Variables

    Distribution Functions

    Discrete Random Variables

    Expectations of Discrete Random Variables

    Variances and Moments of Discrete Random Variables

    Moments

    Standardized Random Variables

    Chapter Summary

    Review Problems

    Self-Test on Chapter

  9. Special Discrete Distributions
  10. Bernoulli and Binomial Random Variables

    Expectations and Variances of Binomial Random Variables

    Poisson Random Variable

    Poisson as an Approximation to Binomial

    Poisson Process

    Other Discrete Random Variables

    Geometric Random Variable

    Negative Binomial Random Variable

    Hypergeometric Random Variable

    Chapter Summary

    Review Problems

    Self-Test on Chapter

  11. Continuous Random Variables
  12. Probability Density Functions

    Density Function of a Function of a Random Variable

    Expectations and Variances

    Expectations of Continuous Random Variables

    Variances of Continuous Random Variables

    Chapter Summary

    Review Problems

    Self-Test on Chapter

  13. Special Continuous Distributions
  14. Uniform Random Variable

    Normal Random Variable

    Correction for Continuity

    Exponential Random Variables

    Gamma Distribution

    Beta Distribution

    Survival Analysis and Hazard Function

    Chapter Summary

    Review Problems

    Self-Test on Chapter

  15. Bivariate Distributions
  16. Joint Distribution of Two Random Variables

    Joint Probability Mass Functions

    Joint Probability Density Functions

    Independent Random Variables

    Independence of Discrete Random Variables

    Independence of Continuous Random Variables

    Conditional Distributions

    Conditional Distributions: Discrete Case

    Conditional Distributions: Continuous Case

    Transformations of Two Random Variables

    Chapter Summary

    Review Problems

    Self-Test on Chapter

  17. Multivariate Distributions
  18. Joint Distribution of n > Random Variables

    Joint Probability Mass Functions

    Joint Probability Density Functions

    Random Sample

    Order Statistics

    Multinomial Distributions

    Chapter Summary

    Review Problems

    Self-Test on Chapter

  19. More Expectations and Variances
  20. Expected Values of Sums of Random Variables

    Covariance

    Correlation

    Conditioning on Random Variables

    Bivariate Normal Distribution

    Chapter Summary

    Review Problems

    Self-Test on Chapter

  21. Sums of Independent Random Variables and Limit Theorems
  22. Moment-Generating Functions

    Sums of Independent Random Variables

    Markov and Chebyshev Inequalities

    Chebyshev’s Inequality and Sample Mean

    Laws of Large Numbers

    Central Limit Theorem

    Chapter Summary

    Review Problems

    Self-Test on Chapter

  23. Stochastic Processes

Introduction

More on Poisson Processes

What Is a Queuing System?

PASTA: Poisson Arrivals See Time Average

Markov Chains

Classifications of States of Markov Chains

Absorption Probability

Period

Steady-State Probabilities

Continuous-Time Markov Chains

Steady-State Probabilities

Birth and Death Processes

Chapter Summary

Review Problems

Self-Test on Chapter

About the Author

Saeed Ghahramani is Professor of Mathematics and Dean of the College of Arts and Sciences at Western New England University. He received his Ph.D. from the University of California at Berkeley in mathematics and is a recipient of teaching awards from Johns Hopkins University and Towson University. His research focuses in applied probability, stochastic processes, and queuing theory.

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis