Product Description

This introduction presents the mathematical theory of probability for readers in the fields of engineering and the sciences who possess knowledge of elementary calculus. Presents new examples and exercises throughout. Offers a new section that presents an elegant way of computing the moments of random variables defined as the number of events that occur. Gives applications to binomial, hypergeometric, and negative hypergeometric random variables, as well as random variables resulting from coupon collecting and match models. Provides additional results on inclusion-exclusion identity, Poisson paradigm, multinomial distribution, and bivariate normal distribution A useful reference for engineering and science professionals.

Product Details

• Amazon Sales Rank: #42518 in Books
• Published on: 2005-05-28
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 576 pages

From the Publisher
A First Course in Probability, Fourth Edition, thoroughly presents the mathematics of probability theory as well as the many diverse applications of the subject. Fundamental concepts such as the principles of combinational analysis, key to computing probabilities, and the axioms of probability theory are thoroughly covered early on. The author's concise writing style and refined textual organization covers topics such as conditional probability and independence of events, conditioning, expectation, and discrete, continuous, and jointly distributed random variables with unparalleled clarity. Interesting exercises and numerous worked examples solidly reinforce concepts.

From the Back Cover
This market-leading introduction to probability features exceptionally clear explanations of the mathematics of probability theory and explores its many diverse applications through numerous interesting and motivational examples. The outstanding problem sets are a hallmark feature of this book. Provides clear, complete explanations to fully explain mathematical concepts. Features subsections on the probabilistic method and the maximum-minimums identity. Includes many new examples relating to DNA matching, utility, finance, and applications of the probabilistic method. Features an intuitive treatment of probability—intuitive explanations follow many examples. The Probability Models Disk included with each copy of the book, contains six probability models that are referenced in the book and allow readers to quickly and easily perform calculations and simulations.

About the Author
Sheldon M. Ross is a professor in the Department of Industrial Engineering and Operations Research at the University of Southern California. He received his Ph.D. in statistics at Stanford University in 1968. He has published many technical articles and textbooks in the areas of statistics and applied probability. Among his texts are A First Course in Probability, Introduction to Probability Models, Stochastic Processes, and Introductory Statistics. Professor Ross is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences, the Advisory Editor for International Journal of Quality Technology and Quantitative Management, and an Editorial Board Member of the Journal of Bond Trading and Management.  He is a Fellow of the Institute of Mathematical Statistics and a recipient of the Humboldt US Senior Scientist Award.

Customer Reviews

Okay for advanced students.
The title of this book is a bit of a misnomer. A more apt title would have been "First Graduate Course in Probability" or "A Second Course in Probability". The book description describes this as an introduction for students with an understanding of only elementary calculus. However, I believe that very few people with a background in only elemetary Calculus are going to be able to follow this text which presupposes facility with proof techniques like mathematical induction and a moderate level of mathematical maturity. Ross does not do any hand holding. Proofs are short and to the point, explanations are terse and compact, "obvious" steps are skipped and left to the reader to fill in. So if you are not prepared to follow terse mathematical explanations that are short on cursory explanation, then this may not be the book for you.

For math majors and other students with a strong mathematics background, however, this may serve as a useful reference. It is concise, elegant and chock full of example problems with solutions. But it all depends on what you are ready for. Some may find the excessive number of example problems distasteful and prefer a less cluttered treatment. Others may find that, despite the examples, the book is not "applied" enough. In my opinion, this book is not suitable as a first course in probability for anyone. You will get the most out of this book if you are already familiar with the subject, or if you have a telented teacher to fill in the numerous gaps. For actuarial students and engineers, you may want to look for a more expository volume like "Introduction to Probability" by Bertsekas.

Sheldon Ross saves me every time
Contrary to its title, this book has helped me through several probability courses. I used this book not only to study for the first actuary exam, but also as a supplement for my intermediate and doctoral-level probability/inference courses. Ross fills in gaps left by texts such as Rice, Cassella and Berger, etc., by spelling out properties of various distributions, and showing how they relate to eachother, and by doing many many examples.

Incidentally, save yourself the money and get an earlier edition. I have the fifth edition, which was not even the current edition at the time that I bought it, and it's perfect as is.

A Classic of Probability Theory
A First Course in Probability by Sheldon Ross covers all the main topics of probability theory: Combinatorics, Probability Axioms, Conditional Probability and Independence, Discrete Random Variables, Continuous Random Variables, Joint Distributions, Expectation, and Limit Theorems. He develops each topic thoroughly using the definition-theorem-proof approach of classical mathematics, interspersed with numerous examples, many of which are classics in probability.

This book does require a solid foundation in calculus. Consequently, it is an appropriate text for a course at an advanced undergraduate level or even a first year graduate course (which is where I first encountered it). It does not require any knowledge of truly advanced mathematics (i.e., measure theory) which one would expect to find in an upper level graduate text, such as Patrick Billingsley's Probability and Measure.

Advice to students (and teachers): A student who does not have a solid foundation in calculus, as evidenced by the ability to apply integration by parts, and perhaps a year of post-calculus math which introduced the concept of the mathematical proof, will have a difficult time with this book.

This book provided me with all the probability theory I needed to complete a master's degree in statistics. Since statistics is nothing more than a collection of applied problems that can be solved, modeled, or at least understood by using the tools of probability theory, I was able to coast through the rest of my master's program and didn't have to start really working again until I subsequently encountered Billingsley's book (cited above).

Thank you, Professor Ross.