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Probability, Statistics, and Stochastic Processes

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ISBN-10: 0470889748

ISBN-13: 9780470889749

Edition: 2nd 2012

Authors: Peter Olofsson, Mikael Andersson

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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…    
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Book details

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: 2.310
Language: English

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
Independent Events
The Law of Total Probability and Bayes' Formula
Bayes' Formula
Genetics and Probability
Recursive Methods
Random Variables
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
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
Joint Distributions
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
Generating Functions
The Probability Generating Function
The Moment Generating Function
The Poisson Process
Thinning and Superposition
Limit Theorems
The Law of Large Numbers
The Central Limit Theorem
The Delta Method
Convergence in Distribution
Discrete Limits
Continuous Limits
Random Number Generation
Simulation of Discrete Distributions
Simulation of Continuous Distributions
Statistical Inference
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
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
Linear Models
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
Goodness of Fit
The Sample Correlation Coefficient
Spearman's Correlation Coefficient
The General Linear Model
Stochastic Processes
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
Martingale Convergence
Stopping Times
Renewal Processes
Asymptotic Properties
Brownian Motion
Hitting Times
Variations of the Brownian Motion
Answers to Selected Problems
Further Reading