Probability, Statistics, and Stochastic Processes

ISBN-10: 0470889748
ISBN-13: 9780470889749
Edition: 2nd 2012
List price: $88.95 Buy it from $85.49
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Description: This book provides a unique and balanced approach to probability, statistics, and stochastic processes.   Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area.  The Second  More...

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Book details

List price: $88.95
Edition: 2nd
Copyright year: 2012
Publisher: John Wiley & Sons, Limited
Publication date: 6/8/2012
Binding: Hardcover
Pages: 576
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 2.002
Language: English

This book provides a unique and balanced approach to probability, statistics, and stochastic processes.   Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area.  The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov–Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and renewal theory.  Many new introductory problems and exercises have also been added.  This book combines a rigorous, calculus–based development of theory with a more intuitive approach that appeals to readers′ sense of reason and logic, an approach developed through the author′s many years of classroom experience.  The book begins with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions. The next two chapters introduce limit theorems and simulation.  Also included is a chapter on statistical inference with a focus on Bayesian statistics, which is an important, though often neglected, topic for undergraduate–level texts.  Markov chains in discrete and continuous time are also discussed within the book.  More than 400 examples are interspersed throughout to help illustrate concepts and theory and to assist readers in developing an intuitive sense of the subject. Readers will find many of the examples to be both entertaining and thought provoking.  This is also true for the carefully selected problems that appear at the end of each chapter.

Preface
Preface to the First Edition
Basic Probability Theory
Introduction
Sample Spaces and Events
The Axioms of Probability
Finite Sample Spaces and Combinatorics
Combinatorics
Conditional Probability and Independence
Independent Events
The Law of Total Probability and Bayes' Formula
Bayes' Formula
Genetics and Probability
Recursive Methods
Problems
Random Variables
Introduction
Discrete Random Variables
Continuous Random Variables
The Uniform Distribution
Functions of Random Variables
Expected Value and Variance
The Expected Value of a Function of a Random Variable
Variance of a Random Variable
Special Discrete Distributions
Indicators
The Binomial Distribution
The Geometric Distribution
The Poisson Distribution
The Hypergeometric Distribution
Describing Data Sets
The Exponential Distribution
The Normal Distribution
Other Distributions
The Lognormal Distribution
The Gamma Distribution
The Cauchy Distribution
Mixed Distributions
Location Parameters
The Failure Rate Function
Uniqueness of the Failure Rate Function
Problems
Joint Distributions
Introduction
The Joint Distribution Function
Discrete Random Vectors
Jointly Continuous Random Vectors
Conditional Distributions and Independence
Independent Random Variables
Functions of Random Vectors
Real-Valued Functions of Random Vectors
The Expected Value and Variance of a Sum
Vector-Valued Functions of Random Vectors
Conditional Expectation
Conditional Expectation as a Random Variable
Conditional Expectation and Prediction
Conditional Variance
Recursive Methods
Covariance and Correlation
The Correlation Coefficient
The Bivariate Normal Distribution
Multidimensional Random Vectors
Order Statistics
Reliability Theory
The Multinomial Distribution
The Multivariate Normal Distribution
Convolution
Generating Functions
The Probability Generating Function
The Moment Generating Function
The Poisson Process
Thinning and Superposition
Problems
Limit Theorems
Introduction
The Law of Large Numbers
The Central Limit Theorem
The Delta Method
Convergence in Distribution
Discrete Limits
Continuous Limits
Problems
Simulation
Introduction
Random Number Generation
Simulation of Discrete Distributions
Simulation of Continuous Distributions
Miscellaneous
Problems
Statistical Inference
Introduction
Point Estimators
Estimating the Variance
Confidence Intervals
Confidence Interval for the Mean in the Normal Distribution with Known Variance
Confidence Interval for an Unknown Probability
One-Sided Confidence Intervals
Estimation Methods
The Method of Moments
Maximum Likelihood
Evaluation of Estimators with Simulation
Bootstrap Simulation
Hypothesis Testing
Large Sample Tests
Test for an Unknown Probability
Further Topics in Hypothesis Testing
P-Values
Data Snooping
The Power of a Test
Multiple Hypothesis Testing
Goodness of Fit
Goodness-of-Fit Test for Independence
Fisher's Exact Test
Bayesian Statistics
Noninformative priors
Credibility Intervals
Nonparametric Methods
Nonparametric Hypothesis Testing
Comparing Two Samples
Nonparametric Confidence Intervals
Problems
Linear Models
Introduction
Sampling Distributions
Single Sample Inference
Inference for the Variance
Inference for the Mean
Comparing Two Samples
Inference about Means
Inference about Variances
Analysis of Variance
One-Way Analysis of Variance
Multiple Comparisons: Tukey's Method
Kruskal-Wallis Test
Linear Regression
Prediction
Goodness of Fit
The Sample Correlation Coefficient
Spearman's Correlation Coefficient
The General Linear Model
Problems
Stochastic Processes
Introduction
Discrete-Time Markov Chains
Time Dynamics of a Markov Chain
Classification of States
Stationary Distributions
Convergence to the Stationary Distribution
Random Walks and Branching Processes
The Simple Random Walk
Multidimensional Random Walks
Branching Processes
Continuous-Time Markov Chains
Stationary Distributions and Limit Distributions
Birth-Death Processes
Queueing Theory
Further Properties of Queueing Systems
Martingales
Martingale Convergence
Stopping Times
Renewal Processes
Asymptotic Properties
Brownian Motion
Hitting Times
Variations of the Brownian Motion
Problems
Tables
Answers to Selected Problems
Further Reading
Index

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