Customer Reviews

A First Course in Probability (6th Edition)

5 star:		(4)
4 star:		(6)
3 star:		(2)
2 star:		(2)
1 star:		(7)

 

 

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.

I used this book (as well as the SOA sample exams) as my sole means of preparation for the Actuary Examination P. Ross does an excellent job of utilizing a plethora of examples in order teach a particular concept. In some cases, a chapter may consist of two pages of instruction, followed by dozens of examples. This method tends to be extremely effective with regard to test preparation, but more frustrating for students using this as a course textbook. The proofs provided are fairly vigorous, but a strong background in Calculus is essential to understanding any significant portion of this book.

The chapter discussing "Jointly Distributed Random Variables" is the longest in the book, and perhaps rightly so, considering this comprises the majority of the P exam. However, in 50 pages of text, about five pages involves a formal discussion of terms and proofs, and the rest is made up of about 40 examples, many which span multiple pages. Again, this happens to be quite effective when paired with the SOA example questions, but may prove to be a difficult text to follow when a professor expects you to understand the finer points of probability theory.

If you can answer every question provided in a sample exam packet, you will easily pass the exam; and you will master the sample exam if you spend several months covering the first seven chapters of this book.

I used this book in my second year of undergrad in an introductory probability course. This book was perfect for such a course. It is a very easy introduction to the world of probability. Ross assumes almost nothing but basic calculus and a willingness to work through the problems to increase your understanding. Some of the other reviews I have read basically are asking for the author to hold your hand and do all the work for you. I felt like this book actually does this a little too much at times, but really strikes an almost perfect balance between simplicity and technical rigor.

Obviously one needs to move on to much more technical and rigorous texts before one actually has an understanding of probability. However, one of the most important abilities I have found in my academic life is the ability to use the basics that I learned in Ross to conceptualize much more difficult concepts. I continually refer back to this book for a intuitive explanation of certain basic concepts when I feel a little rusty during my every day use of probability.

One must be aware though that as my current probability teacher said, probability is inherently challenging, it is not as trivial as calculus. In the sense that our natural world, at a first approximation, follows the laws of Newtonian physics for which calculus was invented; however, probability is much less intuitive and everyone has a difficulty with it at some point or another.

If you manage to solve a good bit of the problems given in this book, you would be more than adequately prepared for an intermediate course in mathematical statistics. The text is uniformly well above average, at least in the earlier chapters. The last two chapters, perhaps the last three, give the reader the impression that they have been added to the book rather grudgingly and as an afterthought. For example, the short chapter on "additional topics in probability" - which deals with Markov chains, coding theory, entropy etc. - hardly does justice to any of the topics dealt with. In spite of these criticisms, this is a decent book on probability at the advanced undergraduate/first year grad. level.

With so many wonderful books available on this subject, I wonder why Mr. Ross felt the need to write this one. It is basically an unintelligible tangle of botched text on what is actually a fairly straightforward and interesting subject. It is unfortunate that this bok is required reading for many undergraduate courses. I can only wonder how many potentially gifted practitioners never persue the subject further because of the bad impression this book leaves. Save your money and your frustration by seeking out any other book on the subject.

HAMMERS probability into your brain. Very good for Financial Math interviews. Challenges the average but slightly smart Math reader just right. Non math guys should get help if the want to LEARN rather than just skipping to an elementaty book. This is not a book on measure theoretic approach.


All the things about the author skipping lot of steps written by the -ve committee are correct so do not buy if you are not using it under guidance.Being a student of Financial Mathematics where all the rigor and the conceptual clearness is necessary TRUST me this guy is an AUTHORITY on the subject.
I am out of touch with math for 10years so in my case I had a Bachelors in Math level person who studied with me - even that person was amazed at the content.

SO,if you have some Masters or atleast Bachelors level person who is helping or learning with you whom you can ask silly or difficult questions then this book is PHENOMENAL. Excellent selection of problems and the touch of history of probability.

Another book is "Probability models"by the same author. That book has a high overlap and less solved probs. If you are a career process scientist or operations research go for the other book . If you want to see problems with nos go for this one. No need to buy both if you are Finmath.

Of all math books I've had, this one is the most poorly written. The style is erratic, some of the least important versions of formulas are boldened, while the ones you actually use may be buried within the text. The examples make non-obvious transformations or 'pull rabbits out of a hat'. The problems are often poorly worded or open to varying interpretation, and the 'solutions' in the back are often just a number like ".30239" for a problem that might have 5 parts and take a whole page to compute. In fact, the solutions of every chapter in the book take merely 3 pages.

Some reviewers say this is one of the best books for beginners in probability, and if that is true, then the world of mathematical instruction is in a sorry state.

This book has all the necessary material for an undergraduate probability text book. The only problem is that the material at times is not well presented. If you have encountered probability before you will find this book helpful, otherwise it might be a bit difficult to follow for those encountering probability for the first time.

That just happened to be what I was usually thinking when I read the book. Several steps in examples are skipped, very little reason for each step is given. Also the formulas are hard to locate some are set off in grey boxes others are blended into the text.

as a student I've found his text confusing and his exercises horridly dumbfounding. I bought 4 other probabity books to understand what he's trying to say. All the other books are better at explaining the examples and in general more patient with the student. If you are a student, buy another book to learn the material.