Basic Probability Theory

by Robert B. Ash

Book Overview

Geared toward advanced undergraduates and graduate students, this introductory text surveys random variables, conditional probability and expectation, characteristic functions, infinite sequences of random variables, Markov chains, and an introduction to statistics. Complete solutions to some of the problems appear at the end of the book. 1970 edition.

• Format: Paperback
• Language: English
• ISBN: 0486466280
• ISBN13: 9780486466286
• Release Date: June 2008
• Publisher: Dover Publications
• Length: 352 Pages
• Weight: 0.80 lbs.
• Dimensions: 0.7" x 5.5" x 8.5"

Customer Reviews

Pretty good book for basic probability theory

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!)

Excellent introduction to probability

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!

Very readable, a jewel

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 is pretty elementary, only requiring knowledge of basic calculus. Incredibly cheap edition by Dover.

Not as basic as you might think

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 6.6 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 yo