Introduction to Probability for Computing

Learn about probability as it is used in computer science with this rigorous, yet highly accessible, undergraduate textbook. Fundamental probability concepts are explained in depth, prerequisite mathematics is summarized, and a wide range of computer science applications is described. Throughout, the material is presented in a “question and answer” style designed to encourage student engagement and understanding. Replete with almost 400 exercises, real-world computer science examples, and covering a wide range of topics from simulation with computer science workloads, to statistical inference, to randomized algorithms, to Markov models and queues, this interactive text is an invaluable learning tool whether your course covers probability with statistics, with stochastic processes, with randomized algorithms, or with simulation. The teaching package includes solutions, lecture slides, and lecture notes for students.

Table of Contents:
Preface; Part I. Fundamentals and Probability on Events: 1. Before we start ... some mathematical basics; 2. Probability on events; Part II. Discrete Random Variables: 3. Probability and discrete random variables; 4. Expectations; 5. Variance, higher moments, and random sums; 6. z-Transforms; Part III. Continuous Random Variables: 7. Continuous random variables: single distribution; 8. Continuous random variables: joint distributions; 9. Normal distribution; 10. Heavy tails: the distributions of computing; 11. Laplace transforms; Part IV. Computer Systems Modeling and Simulation: 12. The Poisson process; 13. Generating random variables for simulation; 14. Event-driven simulation; Part V. Statistical Inference; 15. Estimators for mean and variance; 16. Classical statistical inference; 17. Bayesian statistical inference; Part VI. Tail Bounds and Applications: 18. Tail bounds; 19. Applications of tail bounds: confidence intervals and balls-and-bins; 20. Hashing algorithms; Part VII. Randomized Algorithms: 21. Las Vegas randomized algorithms; 22. Monte Carlo randomized algorithms; 23. Primality testing; Part VIII. Discrete-time Markov Chains; 24. Discrete-time Markov chains: finite-state; 25. Ergodicity for finite-state discrete-time Markov chains; 26. Discrete-time Markov chains: infinite-state; 27. A little bit of queueing theory; References; Index.

About the Author :
Mor Harchol-Balter is the Bruce J. Nelson Professor of Computer Science at Carnegie Mellon University. She is a Fellow of both ACM and IEEE. She has received numerous teaching awards, including the Herbert A. Simon Award for teaching excellence at CMU. She is also the author of the popular textbook Performance Analysis and Design of Computer Systems (Cambridge, 2013).

Review :
'Drawing on more than two decades of teaching experience, the author brings a distinct pedagogical style to the material; one that is rich in illustrative examples, deeply intuitive, and highly accessible. The book is written in a conversational yet rigorous manner, making it suitable for a broad audience without compromising on the mathematical depth required for serious study … One of the standout features of the book is its thoughtfully modular structure. For instance, rather than covering discrete and continuous random variables into two big chapters, the author opts to divide them into nine concise chapters. This approach makes the material more digestible, especially for beginners and practitioners who may be revisiting probability concepts … This book is a great resource for undergraduate students seeking an applied perspective on probability. Among the probability books that I've read, this one has been the most engaging … I thoroughly enjoyed reading the book.' SIGACT News 'Based on 20 years of teaching Computer Science and Operations Research at Carnegie Mellon University, Professor Harchol-Balter provides a unique presentation of probability and statistics that is both highly engaging and also strongly motivated by realworld computing applications that students will encounter in industry. This book is approachable and fun for undergraduate students, while also covering advanced concepts relevant to graduate students.' Eytan Modiano, Massachusetts Institute of Technology 'This book provides a fantastic introduction to probability for computer scientists and computing professionals, addressing concepts and techniques crucial to the design and analysis of randomized algorithms, to performing well-designed simulations, to statistical inference and machine learning, and more. Also contains many great exercises and examples. Highly recommend!' Avrim Blum, Toyota Technological Institute at Chicago 'Mor Harchol-Balter's new book does a beautiful job of introducing students to probability! The book is full of great computer science-relevant examples, wonderful intuition, simple and clear explanations, and mathematical rigor. I love the question-answer style she uses, and could see using this book for students ranging from undergraduate students with zero prior exposure to probability all the way to graduate students (or researchers of any kind) who need to brush up and significantly deepen (and/or broaden) their knowledge of probability.' Anna Karlin, University of Washington 'Probability is at the heart of modeling, design, and analysis of computer systems and networks. This book by a pioneer in the area is a beautiful introduction to the topic for undergraduate students. The material in the book introduces theoretical topics rigorously, but also motivates each topicwith practical applications. This textbook is an excellent resource for budding computer scientists who are interested in probability.' R. Srikant, University of Illinois at Urbana-Champaign 'I know probability theory, and have taught it to undergrads and grads at MIT, UC Berkeley, and Carnegie Mellon University. Yet this book has taught me some wonderfully interesting important material that I did not know. Mor is a great thinker, lecturer, and writer. I would love to have learned from this book as a student - and to have taught from it as an instructor!' Manuel Blum, University of California, Berkeley, and Carnegie Mellon University