reference

Some gaffes in this book, I don't think the author has any real understanding. He even messes up the definition of expectation, and it doesn't get more elementary than that. There are many better probability books out there, don't choose this one.

This book is on the course of reading for the Society of Actuaries and Casualty Actuarial Society jointly sponsored Course 1/Exam 1. Although all the probability books listed on the course of reading are good, this text is probably the one to choose. The book seems to be designed with an actuarial student in mind, and an actuarial student would find it very useful for self study. A solution manual is also available.

The quality and level of the writing are excellent. It covers all the required probability topics, and emphasizes certain topics that are not usually emphasized in other texts. Some of these topics are conditional probability; distributional form of Law of Total Probability and Bayes Theorem; conditional expectation; limited moments; mixed probability distributions; survival distributions; hazard or mortality functions; special continuous distributions used in survival analysis (Weibull, Pareto, etc.); compound Poisson and other compound distributions. All but the last chapter on option pricing would be required reading for Exam 1, and the last chapter useful for Exam 2.

A very useful feature of this textbook is that in Chapters 5 (Special Discrete Distributions) and 6 (Special Continuous Distributions) the distribution theory is very clearly outlined. For example, relationship to other distributions, distribution of iid sums, limiting distributions, etc. are clearly stated and summarized. In addition to Exam 1, this text will also be valuable as a reference to study for Exam 4.

Students who would have difficulty with the level of this presentation will also have difficulty with SOA Exam 1.