Basic Probability Theory

ISBN-10: 0486466280
ISBN-13: 9780486466286
Edition: 2008
Authors: Robert B. Ash
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Description: This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is  More...

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Book details

List price: $22.95
Copyright year: 2008
Publisher: Dover Publications, Incorporated
Publication date: 6/26/2008
Binding: Paperback
Pages: 352
Size: 5.50" wide x 8.50" long x 0.75" tall
Weight: 1.012
Language: English

This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus.

Basic Concepts
Introduction
Algebra of Events (Boolean Algebra)
Probability
Combinatorial Problems
Independence
Conditional Probability
Some Fallacies in Combinatorial Problems
Appendix: Stirling's Formula
Random Variables
Introduction
Definition of a Random Variable
Classification of Random Variables
Functions of a Random Variable
Properties of Distribution Functions
Joint Density Functions
Relationship Between Joint and Individual Densities; Independence of Random Variables
Functions of More Than One Random Variable
Some Discrete Examples
Expectation
Introduction
Terminology and Examples
Properties of Expectation
Correlation
The Method of Indicators
Some Properties of the Normal Distribution
Chebyshev's Inequality and the Weak Law of Large Numbers
Conditional Probability and Expectation
Introduction
Examples
Conditional Density Functions
Conditional Expectation
Appendix: The General Concept of Conditional Expectation
Characteristic Functions
Introduction
Examples
Properties of Characteristic Functions
The Central Limit Theorem
Infinite Sequences of Random Variables
Introduction
The Gambler's Ruin Problem
Combinatorial Approach to the Random Walk; the Reflection Principle
Generating Functions
The Poisson Random Process
The Strong Law of Large Numbers
Markov Chains
Introduction
Stopping Times and the Strong Markov Property
Classification of States
Limiting Probabilities
Stationary and Steady-State Distributions
Introduction to Statistics
Statistical Decisions
Hypothesis Testing
Estimation
Sufficient Statistics
Unbiased Estimates Based on a Complete Sufficient Statistic
Sampling from a Normal Population
The Multidimensional Gaussian Distribution
Tables
A Brief Bibliography
Solutions to Problems
Index

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