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Probability and Statistics for Computer Scientists




ISBN 9781138044487
Published June 14, 2019 by Chapman and Hall/CRC
506 Pages

 
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Book Description

Praise for the Second Edition:

"The author has done his homework on the statistical tools needed for the particular challenges computer scientists encounter... [He] has taken great care to select examples that are interesting and practical for computer scientists. ... The content is illustrated with numerous figures, and concludes with appendices and an index. The book is erudite and … could work well as a required text for an advanced undergraduate or graduate course." ---Computing Reviews

Probability and Statistics for Computer Scientists, Third Edition helps students understand fundamental concepts of Probability and Statistics, general methods of stochastic modeling, simulation, queuing, and statistical data analysis; make optimal decisions under uncertainty; model and evaluate computer systems; and prepare for advanced probability-based courses. Written in a lively style with simple language and now including R as well as MATLAB, this classroom-tested book can be used for one- or two-semester courses.

Features:

  • Axiomatic introduction of probability
  • Expanded coverage of statistical inference and data analysis, including estimation and testing, Bayesian approach, multivariate regression, chi-square tests for independence and goodness of fit, nonparametric statistics, and bootstrap
  • Numerous motivating examples and exercises including computer projects
  • Fully annotated R codes in parallel to MATLAB
  • Applications in computer science, software engineering, telecommunications, and related areas

In-Depth yet Accessible Treatment of Computer Science-Related Topics
Starting with the fundamentals of probability, the text takes students through topics heavily featured in modern computer science, computer engineering, software engineering, and associated fields, such as computer simulations, Monte Carlo methods, stochastic processes, Markov chains, queuing theory, statistical inference, and regression. It also meets the requirements of the Accreditation Board for Engineering and Technology (ABET).

About the Author

Michael Baron is David Carroll Professor of Mathematics and Statistics at American University in Washington D. C. He conducts research in sequential analysis and optimal stopping, change-point detection, Bayesian inference, and applications of statistics in epidemiology, clinical trials, semiconductor manufacturing, and other fields. M. Baron is a Fellow of the American Statistical Association and a recipient of the Abraham Wald Prize for the best paper in Sequential Analysis and the Regents Outstanding Teaching Award. M. Baron holds a Ph.D. in statistics from the University of Maryland. In his turn, he supervised twelve doctoral students, mostly employed on academic and research positions.

Table of Contents

 1. Introduction and Overview
 Making decisions under uncertainty                      
 Overview of this book                              
 Summary and conclusions                               
 Exercises                                        

I Probability and Random Variables

 2. Probability
 Events and their probabilities                         
 Outcomes, events, and the sample space                
 Set operations                              
 Rules of Probability                               
 Axioms of Probability                          
 Computing probabilities of events                   
 Applications in reliability                        
 Combinatorics                                  
 Equally likely outcomes                         
 Permutations and combinations                     
 Conditional probability and independence                   
 Summary and conclusions                               
 Exercises                                        

 3. Discrete Random Variables and Their Distributions
 Distribution of a random variable                       
 Main concepts                              
 Types of random variables                        
 Distribution of a random vector                        
 Joint distribution and marginal distributions             
 Independence of random variables                   
 Expectation and variance                            
 Expectation                                
 Expectation of a function                        
 Properties                                 
 Variance and standard deviation                    
 Covariance and correlation                       
 Properties                                 
 Chebyshev’s inequality                          
 Application to finance                          
 Families of discrete distributions                        
 Bernoulli distribution                          
 Binomial distribution                          
 Geometric distribution                          
 Negative Binomial distribution                     
 Poisson distribution                           
 Poisson approximation of Binomial distribution            
 Summary and conclusions                               
 Exercises                                        

 4. Continuous Distributions
 Probability density                               
 Families of continuous distributions                      
 Uniform distribution                           
 Exponential distribution                         
 Gamma distribution                           
 Normal distribution                           
 Central Limit Theorem                             
 Summary and conclusions                               
 Exercises                                        

 5. Computer Simulations and Monte Carlo Methods
 Introduction                                   
 Applications and examples                       
 Simulation of random variables                         
 Random number generators                       
 Discrete methods                             
 Inverse transform method                        
 Rejection method                             
 Generation of random vectors                      
 Special methods                             
 Solving problems by Monte Carlo methods                  
 Estimating probabilities                         
 Estimating means and standard deviations              
 Forecasting                                
 Estimating lengths, areas, and volumes                
 Monte Carlo integration                         
 Summary and conclusions                               
 Exercises                                        

II Stochastic Processes
 
 6. Stochastic Processes
 Definitions and classifications                          
 Markov processes and Markov chains                     
 Markov chains                              
 Matrix approach                             
 Steady-state distribution                         
 Counting processes                               
 Binomial process                             
 Poisson process                              
 Simulation of stochastic processes                       
 Summary and conclusions                               
 Exercises                                        

 7. Queuing Systems
 Main components of a queuing system                     
 The Little’s Law                                 
 Bernoulli single-server queuing process                    
 Systems with limited capacity                      
 M/M/ system                                  
 Evaluating the system’s performance                  
 Multiserver queuing systems                          
 Bernoulli k-server queuing process                   
 M/M/k systems                             
 Unlimited number of servers and M/M/∞               
 Simulation of queuing systems                         
 Summary and conclusions                               
 Exercises                                        

III Statistics
 
 8. Introduction to Statistics
 Population and sample, parameters and statistics              
 Descriptive statistics                               
 Mean                                   
 Median                                  
 Quantiles, percentiles, and quartiles                  
 Variance and standard deviation                    
 Standard errors of estimates                       
 Interquartile range                            
 Graphical statistics                               
 Histogram                                 
 Stem-and-leaf plot                            
 Boxplot                                  
 Scatter plots and time plots                       
 Summary and conclusions                               
 Exercises                                        

 9. Statistical Inference I
 Parameter estimation                              
 Method of moments                           
 Method of maximum likelihood                     
 Estimation of standard errors                      
 Confidence intervals                               
 Construction of confidence intervals: a general method        
 Confidence interval for the population mean              
 Confidence interval for the difference between two means      
 Selection of a sample size                        
 Estimating means with a given precision                
 Unknown standard deviation                          
 Large samples                               
 Confidence intervals for proportions                  
 Estimating proportions with a given precision             
 Small samples: Student’s t distribution                 
 Comparison of two populations with unknown variances       
 Hypothesis testing                                
 Hypothesis and alternative                       
 Type I and Type II errors: level of significance            
 Level _ tests: general approach                     
 Rejection regions and power                       
 Standard Normal null distribution (Z-test)              
 Z-tests for means and proportions                   
 Pooled sample proportion                        
 Unknown _: T-tests                           
 Duality: two-sided tests and two-sided confidence intervals      
 P-value                                  
 Inference about variances                            
 Variance estimator and Chi-square distribution            
 Confidence interval for the population variance            
 Testing variance                             
 Comparison of two variances F-distribution             
 Confidence interval for the ratio of population variances       
 F-tests comparing two variances                    
 Summary and conclusions                               
 Exercises                                        

 10. Statistical Inference II
 Chi-square tests                                 
 Testing a distribution                          
 Testing a family of distributions                    
 Testing independence                          
 Nonparametric statistics                            
 Sign test                                  
 Wilcoxon signed rank test                        
 Mann-Whitney-Wilcoxon rank sum test                
 Bootstrap                                     
 Bootstrap distribution and all bootstrap samples           
 Computer generated bootstrap samples                
 Bootstrap confidence intervals                      
 Bayesian inference                                
 Prior and posterior                            
 Bayesian estimation                           
 Bayesian credible sets                          
 Bayesian hypothesis testing                       
 Summary and conclusions                               
 Exercises                                        

 11. Regression
 Least squares estimation                            
 Examples                                 
 Method of least squares                         
 Linear regression                             
 Regression and correlation                        
 Overfitting a model                           
 Analysis of variance, prediction, and further inference            
 ANOVA and R-square                          
 Tests and confidence intervals                      
 Prediction                                 
 Multivariate regression                             
 Introduction and examples                       
 Matrix approach and least squares estimation             
 Analysis of variance, tests, and prediction               
 Model building                                  
 Adjusted R-square                            
 Extra sum of squares, partial F-tests, and variable selection     
 Categorical predictors and dummy variables              
 Summary and conclusions                               
 Exercises                                        

IV Appendix
 
12. Appendix

 Data sets                                     
 Inventory of distributions                            
 Discrete families                             
 Continuous families                           
 Distribution tables                                
 Calculus review                                 
 Inverse function                              
 Limits and continuity                          
 Sequences and series                           
 Derivatives, minimum, and maximum                 
 Integrals                                  
 Matrices and linear systems                           
 Answers to selected exercises                          

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Author(s)

Biography

Michael Baron is a professor of statistics at the American University in Washington, DC. He has published two books and numerous research articles and book chapters. Dr. Baron is a fellow of the American Statistical Association, a member of the International Society for Bayesian Analysis, and an associate editor of the Journal of Sequential Analysis. In 2007, he was awarded the Abraham Wald Prize in Sequential Analysis. His research focuses on the use of sequential analysis, change-point detection, and Bayesian inference in epidemiology, clinical trials, cyber security, energy, finance, and semiconductor manufacturing. He received a Ph.D. in statistics from the University of Maryland.

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