Customer Reviews

Basic Probability Theory (Dover Books on Mathematics)

5 star:		(5)
4 star:		(0)
3 star:		(1)
2 star:		(0)
1 star:		(1)

 

 

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 Generāl 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
6.6 The Strong Law of Large Numbers
7. MARKOV CHAINS
7.1 Introduction
7.2 Stopping Times and the Strong Markov Property
7.3 Classification of States
7.4 Limiting Probabilities
7.5 Stationary and Steady-State Distributions


8. INTRODUCTION TO STATISTICS

8.1 Statistical Decisions
8.2 Hypothesis Testing
8.3 Estimation
8.4 Sufficient Statistics
8.5 Unbiased Estimates Based on a Complete Sufficient Statistic
8.6 Sampling from a Normal Population
8.7 The Multidimensional Gaussian Distribution
Tables
A Brief Bibliography

Solutions to Problems

This book is an excellent introduction that stops short of
doing a measure-theoretic treatment of probability theory, but it does
bring the concepts up. It is aimed at the person who likes a theoretic theorem-proof approach with all steps spelled out (again with the proviso that
it does not go into detail so far as constructing measures etc), so it does require more mathematical maturity than what you would expect in first year university students.
It might be called an "intermediate level course in probability theory".
When you have read this I recommend you move up to the same author's book Probability & Measure Theory, Second Edition which is very clear too and generous with detail just like this one.
It seems obvious when reading this that the author loves teaching and is like a friend standing over your shoulder helping you.

There are 43 pages of solutions to problems, so this is very helpful.

My only niggle is that the author does not deal with hazard rates which are much used in engineering.

The value for money is fantastic.

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.

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!)

Don't be fooled by the back cover or the first line of the preface - this is NOT an "introduction" in any sense of the word, and neither is it appropriate for a "first course in probability". Not only does the author fail to adequately explain or introduce new topics, he does not even define his symbology. How is a reader supposed to understand an expression if we aren't even told what the symbols used in it are supposed to mean?

In short, if you are not already intimately familiar with the subjects and need no explanations, this is not the book for you.

This book is well-written and a good introduction to probability theory. There isn't a class taught at my local college on this subject, yet it's used in so many other math classes!

This is a great book, thin enough and hence not too intimidating. It covers some basic theory, and very readable.

I have Ash's IEEE books on Calculus, and Probability. They are outstanding companions to what ever text you use for those subjects. They are good references for refreshing knowledge. This book is not them. It is written more for an accademic. If you want theory and proof from Dr. Ash, this is it. I would use this one and the IEEE book on Probability together.