This book is best for those with some exposure to probability and statistics. If you've had science courses that used probability but you've never actually taken a probability course, then this book could be perfect.
In my opinion, this text provides a strong foundation. It makes books like All of Statistics: A Concise Course in Statistical Inference (Springer Texts in Statistics), easier to use and harder to abuse.
- Clarity: There are no missing steps in the math, you don't have to doodle in the margins to derive the next equation.
- Mathematical ease: This is calculus-based probability but the calculus is not difficult and the algebra is crystal clear.
- Completeness: The book clearly presents core concepts concisely; it is not telegraphic. You will be introduced to probability distributions, conditional probability, Markov models, queuing theory, stochastic processing and methods for simulating distributions.
- Theory: The text mentions or proves relevant theorems at the rate of 1 every 10 pages. The proofs were simple and the theorems are crucial - for introductory texts, that counts as theory for me.
- Examples: There are many good examples that make it more memorable.
- Structure: Overall, I thought the structure was good. As a novice, I particularly liked the 2nd chapter on random variables - a clean approach to various probability distributions, their parameters and functions. As a scientist, I was grateful for the clear introduction to queues and stochastic processes.
Other reviewers have complained about structure and, since this doesn't really make sense, I am guessing that it comes from failed expectations. This is not a introduction to statistics. You won't find the Wald test, Bayesian testing, Pearson's chi-squared, a likelihood ratio test or any other workaday statistical test. If that is what you want, then go to "All of Statistics" (see above).
- Graphics (or lack thereof): I could have used more figures. Out of curiosity, I wrote a program to see probability density functions for different parameters and variables. Markov chains without actual transition diagrams seemed odd.
- Odd-man-out chapters: I didn't really understand the inclusion of the Reliability chapter (probably just me).
- Redundant/simple examples: For example, the Renewal chapter had near identical examples(in one, lightbulbs blown out, in another, batteries depleted) but nothing more compelling - what about evolution?? Mutation is a Poisson process, but sometimes the mutation creates a selective sweep which is a renewal process, so what kind of process is evolution? Horse kicks are Poisson but if you replace the horse every time it kicks someone, then that's renewal. So what's the likelihood of a horse kick with renewal? I would have enjoyed some more complicated examples.
Nitpicking aside, I thought this was a great book.