Introduction to Probability Theory and Statistical Inference

This is a great introductory text in calculus-based probability and the central concepts of mathematical statistics. I have taught two one semester courses at this level using other books, and if I teach such a course again, I will be using this book. One of the other books that I used was Devore's "Probability and Statistics for Engineers and Science." I did not care for Devore's book. Devore does not fully develop many of the calculus-based ideas of probability distributions, and he uses very poor and non-standard notation. Larson is very clear, and uses solid notation that a student will see time-and-time again if she takes more advanced courses. It doesn't make sense to offer "introductory" courses which do not properly prepare the student for "intermediate" courses. This book is easily the best available option for a one semester introductory course in probability and statistics. Cons for this book. (1) This book is very pricey for a paperback book. Rebuttal: Lots of textbooks are pricey. Here you spend a little too much money, but you get a book that is worth keeping. However, I do think this book should cost less. (2) The book is old. Rebuttal: The basic ideas of probability and statistics do not change in time. Also, this should cast shame on the newer textbooks which are not very good. (3) This book does not have a lot of problems. Rebuttal: Very true. You will have to LaTeX weekly problem sets for your students. Casella and Berger has a large number of problems with varied levels of difficulty, and there is a problem book for Cox and Hinkley. Pick some out and give them to the students. Tell the students that they should be working the book problems as practice. If you need a book for a two semester introduction to probability and statistics, you should consider "Mathematical Statistics and Data Analysis" by John Rice.

Is there any advanced studant of probability theory who does not know this book?? Certainly not!! But, If you are at college and need a book on probability theory, Larson is a very good option. The chapters 1 to 4 are perfect if you know calculus and do not know anything about probability. I think it is important to say that you pay for 11 chapters, but just 4 or 5 are really good (the scond part is not so good as the first). Again, I should repeat: Of course, it is a undergraduate book, as everybody knows.

The last reviewer must be kidding or he do not understand so much about probability. Ok, this book is great, no questions. But this is definitely a introductory probability and statistical inference book. Going further to the probability portion, we could say that it is intended to "Calculus of Probability", not Probability theory. So, we must be clear about the books that are for sale. Advanced texts can be encountered in Chung, Billlingsley, Feller and others. Not this here, nor even DeGroot!! About rigorousness, we can see that Larson's book is rigorous until Differential and Integral Calculus (not analysis!!!!!!) allows it to be. This attribute is the one that assures the introductory profile to the book. Period.

I studied with this book at the university. The first 4 chapters are a perfect (in a didactic viewpoint) introduction to (a formal and rigorous) probability theory. Not so good in teaching random vectors (R², R³ etc.), has two good chapters for inference (a really good introduction, but not a full presentation). OBS: forget Bayesian and nonparametric methods. The chapters dedicated to this subjects are not that good.