Probability: For the Enthusiastic Beginner

The subtitle "For the Enthusiastic Beginner", may imply to some that this is an elementary book, but it is not. The subtitle refers to the fact that the subject is covered from the beginning with no required calculus (although some is used optionally). While not focusing on theorems and derivations, some are developed. The focus of the book is on understanding the basics of probability, with only a minimal amount of rigorous mathematical formalism. This is not to say that this is a slimmed down treatment devoid of formal mathematics, it is not.As with the other of Morin's books this is another great teaching book. It is clearly written, includes a large number of solved problems and is a good choice as a self-education text, as well as a course textbook or adjunct to book used in a class. My only complaint is that I would have liked even more solved problems. Most of the solved problems are challenging and are included as illustrations of particular points, as opposed to giving the reader simpler problems in order to gain experience with applying the material in the book.What is in the book:Chapter 1 - Combinatorics - Determining how various combinations are computed (counting with and without repetitions and for ordered and disordered sets.)Chapter 2 - Probability - The definition of probability and determinations of "and" and "or" combinations, plus Bayes' theorem, Stirlings's formula.Chapter 3 - Expectation values, variance, standard deviation.Chapter 4 - Distributions (Uniform, Bernoulli, Binomial, Exponential, Poisson and Gaussian.Chapter 5 - The Gaussian Approximations, law of large numbers, central limit theorem.Chapter 6 - Correlation and Regression - Definition of correlation, correlation coefficient, regression lines.Appendices - Subtleties about probability, Euler's number, approximation, important results, glossary.

My son needed this for college, but I have enjoyed reading it also. It helped me in my ACT Prep business too!

It starts with plenty of combinatorics practice to develop a facility for counting, which is a necessary foundation for the probability chapter, all with thorough explanations of the math. And then basic statistics. And I like the appendix on Euler's number and a compound interest example.

Overall, the presentation of probability as a subject is very thoughrough and well done. Probability is an unintuitive and confusing subject for many and the author does a good job of walking through many examples solved in various different methods and explaining in much detail.Here come the caveats. The author uses the term "Expectation value" when he refers to the "Expected value" or simply the "Expectation". The latter two are the accepted terminology used in the subject of Probability to describe the probability weighted average of a random variable. The former term, "Expectation value", which the author uses repeatedly is only used in Quantum Mechanics. Although they measure pretty the same thing, it is bothersome that the author used a Physics terminology in a Probability textbook instead of following the convention. This probably has something to do with the author's background in Physics.Secondly, the author uses some unconventional notations for combinatorics formulas. For the formula to calculate the number of possibilities in multiple i.i.d. random experiments, the author shows a formula N^n where N is the number of possible outcomes in a single experiment and n is the number of times the experiment is repeated. Generally, in Probability, either the letter "k" or "r" is used in place of n. N^n only has two letters so it may be ok but when you go to the more complicated formulas like N! / n!(N-n)! or (n+N-1)! / n!(N-1)! it becomes confusing especially when you try to remember the formulas by saying them in your head (n factorial divided by n factorial times n minus n factorial). You would have to remember which ones are big N and which are small n and maybe even say them explicitly in your head i.e. big N factorial divided by small n factorial times big N minus small n factorial. These confusions are easily avoided in conventional Probability by using the letters "k" or "r" instead. These are a couple of caveats are things to be improved possibly in the next edition. It's a shame that the terminologies and notations are throwing one off in an otherwise very good introductory Probability textbook.