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Basic Probability Theory (Dover Books on Mathematics) Paperback – June 26, 2008

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Robert B. Ash (Author)
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4.3 out of 5 stars 16 customer reviews
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 352 pages
  • Publisher: Dover Publications (June 26, 2008)
  • Language: English
  • ISBN-10: 0486466280
  • ISBN-13: 978-0486466286
  • Product Dimensions: 8.5 x 5.5 x 0.7 inches
  • Shipping Weight: 10.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #400,001 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

158 of 159 people found the following review helpful
Not as basic as you might think
By M. Henri De Feraudy on November 16, 2008
Format: Paperback
There is no "Look inside" displayed for this book, so here is a copy of the table of contents.
1. BASIC CONCEPTS
1.1 Introduction
1.2 Algebra of Events (Boolean Algebra)
1.3 Probability
1.4 Combinatorial Problems
1.5 Independence
1.6 Conditional Probability
1.7 Some Fallacies in Combinatorial Problems
1.8 Appendix: Stirling's Formula

2. RANDOM VARIABLES
2.1 Introduction
2.2 Definition of a Random Variable
2.3 Classification of Random Variables
2.4 Functions of a Random Variable
2.5 Properties of Distribution Functions
2.6 Joint Density Functions
2.7 Relationship Between Joint and Individual Densities;
Independence of Random Variables
2.8 Functions of More Than One Random Variable
2.9 Some Discrete Examples

3.EXPECTATION
3.1 Introduction
3.2 Terminology and Examples
3.3 Properties of Expectation
3.4 Correlation
3.5 The Method of Indicators
3.6 Some Properties of the Normal Distribution

3.7 Chebyshev's Inequality and the Weak Law of Large Numbers

4.CONDITIONAL PROBABILITY AND EXPECTATION
4.1 Introduction
4.2 Examples
4.3 Conditional Density Functions
4.4 Conditional Expectation
4.5 Appendix: The Generâl Concept of Conditional Expectation
5.CHARACTERISTIC FUNCTIONS

5.1 Introduction
5.2 Examples
5.3 Properties of Characteristic Functions
5.4 The Central Limit Theorem
6. INFINITE SEQUENCES OF RANDOM VARIABLES
6.1 Introduction
6.2 The Gambler's Ruin Problem
6.3 Combinatorial Approach to the Random Walk; the Reflection
Principle
6.4 Generating Functions
6.5 The Poisson Random Process
6.Read more ›
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52 of 55 people found the following review helpful
Very readable, a jewel
By J. R. G. Mendonca on December 5, 2008
Format: Paperback
I studied the basics of probability from this book and I reccomend it to anyone interested in the subject. At that time (epoch...) I simply found the book by Feller too wordy and large and took this one as an alternative and I must say it did the job finely. It is not 'for dummies,' but it is very readable and complete with all steps necessary to understand the ideas and techniques presented. I disagree a little bit with an other reviewer that stated that this book is sort of an intermediate level text - it only requires knowledge of single-variable calculus. Incredibly cheap edition by Dover.
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37 of 38 people found the following review helpful
Pretty good book for basic probability theory
By Ko Chang Su on February 14, 2010
Format: Paperback
This is a small book.
Actually, if you want to grab a book that can cover the whole material about probability, this won't be a good choice.
However, just as the first step to study probability, I think this book is a good choice.

There is a solution for odd number exercises in this book.
(If you search the webpage of author, you check other solutions for even number!)
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6 of 6 people found the following review helpful
Best book to learn Probability for Engineers
By A Singh on December 9, 2012
Format: Paperback Verified Purchase
Luckily I bought this book based on a previous review and i can say that this is the best book (life savior) "for engineers" trying to learn Probability concepts.
It does not cover measure theory (touches lightly at some places) but approaches continous probability from Riemann integral approach - so this is a basic probability book.
I have been out of school for over 10 years and this puts me right at home. I have tried several other books and none came close to this one. Mathematicians will probably have a different opinion.
The book has worked out examples and solutions at the end. Primary aim of the author is for the reader to understand the concepts.
I am going to buy all other topics by the author whether I need them right away or not.
I just like to support good authors, which are so rare :). By the way this book is available for free download from uiuc website i think, if you want to evaluate.
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5 of 6 people found the following review helpful
Not too basic.
By Thanawath1978 on October 27, 2012
Format: Paperback
The book is well written and its content is very good. Although it is free from measure theory, I don't think that only calculus is enough in order to read this book smoothly. (as it is advertised)

This is the only reason why I do not give this book five stars.

You have to have some background knowledge of advanced mathematics beyond calculus. For those who do not hold degree in mathematics, I recommend you to read "Introduction to Analysis" by Maxwell Rosenlicht as a companion. The book is readable and very helpful and also from Dover, so it is cheap and concise.
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5 of 6 people found the following review helpful
Good book requiring alot of concentration but excellent, smooth intro
By Josh on March 4, 2012
Format: Paperback Verified Purchase
Although at first the book is off-putting because of the small print, I found the book to be the best resource I have for intro to probability and mathematical stats. The exercises are perfect and slowly build the reader's understanding. I think what all probability and stat books are missing are pictures/diagrams/graphs, so compared to other books it is doing well...still would like more pics.
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3 of 4 people found the following review helpful
This is where you start from
By Abe on January 3, 2014
Format: Paperback Verified Purchase
I think after searching for many books, I have found the book which will direct me all way through the statistics major.
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2 of 4 people found the following review helpful
We tried to like this book, but ....
By Gets Around on January 29, 2015
Format: Paperback Verified Purchase
We tried to use this book for our mini-course we're running on probability for my colleagues in the lab. We need this stuff for data analysis in a biology lab, where the statistical methods get extremely complex. However, we had to abandon it by chapter two and find another book. There is some great material and exercises. And the author tries to bring things down to earth with long bits of motivation. But we found the long sojourns were just adding confusion and not helping. We found the book tried too hard to be rigorous with the whole issue of non-measurable sets and sigma-algebras, but it was just laid out in a far too convoluted and confusing manner that just frustrated the students. I would chalk this up to the nature of the subject except that I was able to distill the material into a much more palatable presentation for each section. I was able to get to the point and bullet-point out a clear road map to get their heads around the material, and without doing that they were completely lost. And these are smart people with higher degrees, masters and PhDs and they have all the calculus background necessary, we even spent a year reviewing calculus with all the proofs, just before reading this book. We are now going to use Harold Larson's book on probability instead, which side-steps the whole sigma-algebra thing altogether.
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