Customer Reviews

Probability: An Introduction

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Okay it's dover so that means two things: 1) it's cheap (sometimes this equates to value, sometimes not) and 2) It's no the most current book in the world. Nevertheless, this is still a quite useful book.

It is, as the name suggests, an intoduction to probability.
Topic included are:

1) Set theory- examples of sets and set notation, subsets, operatons on sets, algebra of sets, cartesian product sets (about 40 pages)
2) Probability in finite sample spaces- samples spaces, events, probability of an event, some probability theorems, conditional probability, bayes' formula. independent events, independence of several events, independent trials, a probability model in genetics (about 85 pages)

3) Sophisticated counting- counting techniques, binomial coefficients (about 25 pages)

4) Random variables: Random variables and probability functions, mean of a random variable, variance and standard deviation, joint probability functions, means and variance of sums of random variables, covariance and correlation (about 100 pages)

5) Binomial Distribution and some applications: bernoulli trials and binomial distribution, testing a hypothesis, an examples of decision making under uncertainty (about 40 pages)

As you can clearly see, there is no normal distribution. Also the book has answers (not worked) to only odd numbered questions. The problems are quite tricky at times and do require some thought. The author's style is quite readable, showing the lessening of stiltedness that seem to afflict books of it's era. Mathematical formalism isn't at the forefront of what the author is trying to do: he's trying to teach you how it works, rather than how to prove it from first principles. This means it isn't a bad book for the beginner. No calculus is required. And obviously the meat of the book is on the treatment of random variables and typical descriptive measures: mean, variance, standard deviation, covariance, correlation.

I have to admit that I enjoyed working through the book as it isn't enormous or burdened with irrelevant crapola. While I would have liked further treatement of the normal distribution, what this book gives is quite excellent for the price and size of the book. Paul Pfeiffer's 'concepts of probability Theory'(isbn 0486636771) makes a good continuation to this book if you are learning at your own pace, rather than inside a structured course.

All in all, a good little book that offers good value and doesn't promise the world but fail to devliver: it promises an introduction and that's what you get: a basic introduction (though it requires some effort, so it perhaps isn't as introductory as it might seems- depends on your mathematical ability). If you're working with the normal distrubution or wanting a 'cookbook' on probability, however, look elsewhere. This book teaches more through exposition then by example.

Compared to the average book on this subject on the market, this book is a gem. When you add its very low price (as I write this, a used copy is under $2 + shipping on Amazon.com), you get two gems. You count how many gems you get when you add these points:

1) It presents the version of the probability theory that is firmly based on sample spaces. Consequently, and very importantly, a random variable is defined as a real-valued function on a sample space, which makes a lot more sense than the typical definition you will find in the terribly overpriced, overcolored and overly dumbed down modern college-statistics books, in which a random variable is defined as a "variable (a concept that is not defined in these books, btw) that takes chance values". Actually, Goldberg tells you that the name "random variable" is singularly inappropriate for something that is not random, nor a variable. You will also learn the Bayes' theorem, which is shamefully placed in footnotes or even completely omitted by many all-shiny new books.

2) This guy can teach and so can his book! It will take you from step one to step one hundred without ever giving you the impression that he's just skipped a few steps in a hurry to get to the next topic. It does not jump ahead, and it does not lag either: you won't find tons of examples and exercises that add nothing to the previous ones but make the book thicker and more expensive.

Each example and exercise has a purpose, either to introduce a new concept or a particular case or to make you use another theorem to solve it. There are no hard or tricky exercises here, you only need to have read the section carefully. Almost every theorem or definition is introduced or followed by one example or two. Goldberg tells you all and only what you need to know to fully understand what you are doing; no more, and no less.

I found only one bug: a few concepts are introduced by even-numbered exercises at the end of the sections. Given that the book provides answers only to odd-numbered exercises, you cannot verify your understanding of those concepts. Fortunately, there are only one or two such cases in each section, and those concepts are not needed later in the book.

Also, don't forget that this is a book on discrete probability only. There is no place for the normal distribution, nor for any topics in statistics, apart from a formal introduction to populations and samples with replacement, both of which can be defined using random variables and their distributions -- did you know that?

Although it does not cover continuous probability, this book will give you basic, important concepts and material needed for a college level undergraduate course in Mathematical Statistics. Be aware that even though there is no use of differential and integral calculus, the book still requires you to be able to learn the algebra of sets on your own if you do not already know it, to be good at algebraic manipulation, and to have a decent level of mathematical sophistication. Problems range from easy to extremely hard, but do not let it discourage you if you are unable to solve the difficult problems.

This book is an excellent introduction to probability. Not too fond of the "old" English, but the core content is top-notched. Easy to follow. Good examples of concepts. However, since this is an introductory book, don't expect too much of the advanced materials.