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Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields.
Beginning with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions, the book goes on to present limit theorems and simulation. The authors combine a rigorous, calculus-based development of theory with an intuitive approach that appeals to readers' sense of reason and logic. Including more than 400 examples that help illustrate concepts and theory, the Second Edition features new material on statistical inference and a wealth of newly added topics, including:
Consistency of point estimators
Large sample theory
Bootstrap simulation
Multiple hypothesis testing
Fisher's exact test and Kolmogorov-Smirnov test
Martingales, renewal processes, and Brownian motion
One-way analysis of variance and the general linear model
Extensively class-tested to ensure an accessible presentation, Probability, Statistics, and Stochastic Processes, Second Edition is an excellent book for courses on probability and statistics at the upper-undergraduate level. The book is also an ideal resource for scientists and engineers in the fields of statistics, mathematics, industrial management, and engineering.
Preface to the First Edition
Basic Probability Theory
Sample Spaces and Events
The Axioms of Probability
Finite Sample Spaces and Combinatorics
Conditional Probability and Independence
The Law of Total Probability and Bayes’ Formula
Problems
Random Variables
Discrete Random Variables
Continuous Random Variables
Expected Value and Variance
Special Discrete Distributions
The Exponential Distribution
The Normal Distribution
Other Distributions
Location Parameters
The Failure Rate Function
Problems
Joint Distributions
The Joint Distribution Function
Discrete Random Vectors
Jointly Continuous Random Vectors
Conditional Distributions and Independence
Functions of Random Vectors
Conditional Expectation
Covariance and Correlation
The Bivariate Normal Distribution
Multidimensional Random Vectors
Generating Functions
The Poisson Process
Problems
Limit Theorems
The Law of Large Numbers
The Central Limit Theorem
Convergence in Distribution
Problems
Simulation
Random Number Generation
Simulation of Discrete Distributions
Simulation of Continuous Distributions
Miscellaneous
Problems
Statistical Inference
Point Estimators
Confidence Intervals
Estimation Methods
Hypothesis Testing
Further Topics in Hypothesis Testing
Goodness of Fit
Bayesian Statistics
Nonparametric Methods
Problems
Linear Models
Sampling Distributions
Single Sample Inference
Comparing Two Samples
Analysis of Variance
Linear Regression
The General Linear Model
Problems
Stochastic Processes
Discrete -Time Markov Chains
Random Walks and Branching Processes
Continuous -Time Markov Chains
Martingales
Renewal Processes
Brownian Motion
Problems
Appendix A Tables
Appendix B Answers to Selected Problems
Further Reading