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## Book Description

Student-Friendly Coverage of Probability, Statistical Methods, Simulation, and Modeling Tools
Incorporating feedback from instructors and researchers who used the previous edition, Probability and Statistics for Computer Scientists, Second Edition helps students understand general methods of stochastic modeling, simulation, and data analysis; make optimal decisions under uncertainty; model and evaluate computer systems and networks; and prepare for advanced probability-based courses. Written in a lively style with simple language, this classroom-tested book can now be used in both one- and two-semester courses.

New to the Second Edition

• Axiomatic introduction of probability
• Expanded coverage of statistical inference, including standard errors of estimates and their estimation, inference about variances, chi-square tests for independence and goodness of fit, nonparametric statistics, and bootstrap
• More exercises at the end of each chapter
• Additional MATLAB® codes, particularly new commands of the Statistics Toolbox

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).

Encourages Practical Implementation of Skills
Using simple MATLAB commands (easily translatable to other computer languages), the book provides short programs for implementing the methods of probability and statistics as well as for visualizing randomness, the behavior of random variables and stochastic processes, convergence results, and Monte Carlo simulations. Preliminary knowledge of MATLAB is not required. Along with numerous computer science applications and worked examples, the text presents interesting facts and paradoxical statements. Each chapter concludes with a short summary and many exercises.

1. Preliminaries
2. Dedication
3. Preface
4. Chapter 1 Introduction and Overview
1. 1.1 Making decisions under uncertainty
2. 1.2 Overview of this book
3. Summary and conclusions
4. Exercises
5. Part I Probability and Random Variables
1. Chapter 2 Probability
1. 2.1 Events and their probabilities
2. 2.2 Rules of Probability
1. 2.2.1 Axioms of Probability
2. 2.2.2 Computing probabilities of events
3. 2.2.3 Applications in reliability
3. 2.3 Combinatorics
1. 2.3.1 Equally likely outcomes
2. 2.3.2 Permutations and combinations
4. 2.4 Conditional probability and independence
5. Summary and conclusions
6. Exercises
2. Chapter 3 Discrete Random Variables and Their Distributions
1. 3.1 Distribution of a random variable
2. 3.2 Distribution of a random vector
3. 3.3 Expectation and variance
4. 3.4 Families of discrete distributions
5. Summary and conclusions
6. Exercises
3. Chapter 4 Continuous Distributions
1. 4.1 Probability density
2. 4.2 Families of continuous distributions
1. 4.2.1 Uniform distribution
2. 4.2.2 Exponential distribution
3. 4.2.3 Gamma distribution
4. 4.2.4 Normal distribution
3. 4.3 Central Limit Theorem
4. Summary and conclusions
5. Exercises
4. Chapter 5 Computer Simulations and Monte Carlo Methods
1. 5.1 Introduction
2. 5.2 Simulation of random variables
1. 5.2.1 Random number generators
2. 5.2.2 Discrete methods
3. 5.2.3 Inverse transform method
4. 5.2.4 Rejection method
5. 5.2.5 Generation of random vectors
6. 5.2.6 Special methods
3. 5.3 Solving problems by Monte Carlo methods
1. 5.3.1 Estimating probabilities
2. 5.3.2 Estimating means and standard deviations
3. 5.3.3 Forecasting
4. 5.3.4 Estimating lengths, areas, and volumes
5. 5.3.5 Monte Carlo integration
4. Summary and conclusions
5. Exercises
6. Part II Stochastic Processes
1. Chapter 6 Stochastic Processes
1. 6.1 Definitions and classifications
2. 6.2 Markov processes and Markov chains
1. 6.2.1 Markov chains
2. 6.2.2 Matrix approach
3. 6.3 Counting processes
1. 6.3.1 Binomial process
2. 6.3.2 Poisson process
4. 6.4 Simulation of stochastic processes
5. Summary and conclusions
6. Exercises
2. Chapter 7 Queuing Systems
1. 7.1 Main components of a queuing system
2. 7.2 The Little’s Law
3. 7.3 Bernoulli single-server queuing process
1. 7.3.1 Systems with limited capacity
4. 7.4 M/M/1 system
1. 7.4.1 Evaluating the system’s performance
5. 7.5 Multiserver queuing systems
1. 7.5.1 Bernoulli k-server queuing process
2. 7.5.2 M/M/k systems
3. 7.5.3 Unlimited number of servers and M/M/∞
6. 7.6 Simulation of queuing systems
7. Summary and conclusions
8. Exercises
7. Part III Statistics
1. Chapter 8 Introduction to Statistics
1. 8.1 Population and sample, parameters and statistics
2. 8.2 Simple descriptive statistics
1. 8.2.1 Mean
2. 8.2.2 Median
3. 8.2.3 Quantiles, percentiles, and quartiles
4. 8.2.4 Variance and standard deviation
5. 8.2.5 Standard errors of estimates
6. 8.2.6 Interquartile range
3. 8.3 Graphical statistics
1. 8.3.1 Histogram
2. 8.3.2 Stem-and-leaf plot
3. 8.3.3 Boxplot
4. 8.3.4 Scatter plots and time plots
4. Summary and conclusions
5. Exercises
2. Chapter 9 Statistical Inference I
1. 9.1 Parameter estimation
1. 9.1.1 Method of moments
2. 9.1.2 Method of maximum likelihood
3. 9.1.3 Estimation of standard errors
2. 9.2 Confidence intervals
3. 9.3 Unknown standard deviation
4. 9.4 Hypothesis testing
1. 9.4.1 Hypothesis and alternative
2. 9.4.2 Type I and Type II errors: level of significance
3. 9.4.3 Level &#945; tests: general approach
4. 9.4.4 Rejection regions and power
5. 9.4.5 Standard Normal null distribution (Z-test)
6. 9.4.6 Z-tests for means and proportions
7. 9.4.7 Pooled sample proportion
8. 9.4.8 Unknown &#963;: T-tests
9. 9.4.9 Duality: two-sided tests and two-sided confidence intervals
10. 9.4.10 P-value
1. 9.5.1 Variance estimator and Chi-square distribution
2. 9.5.2 Confidence interval for the population variance
3. 9.5.3 Testing variance
4. 9.5.4 Comparison of two variances. F-distribution.
5. 9.5.5 Confidence interval for the ratio of population variances
6. 9.5.6 F-tests comparing two variances
6. Summary and conclusions
7. Exercises
3. Chapter 10 Statistical Inference II
1. 10.1 Chi-square tests
2. 10.2 Nonparametric statistics
1. 10.2.1 Sign test
2. 10.2.2 Wilcoxon signed rank test
3. 10.2.3 Mann-Whitney-Wilcoxon rank sum test
3. 10.3 Bootstrap
1. 10.3.1 Bootstrap distribution and all bootstrap samples
2. 10.3.2 Computer generated bootstrap samples
3. 10.3.3 Bootstrap confidence intervals
4. 10.4 Bayesian inference
1. 10.4.1 Prior and posterior
2. 10.4.2 Bayesian estimation
3. 10.4.3 Bayesian credible sets
4. 10.4.4 Bayesian hypothesis testing
5. Summary and conclusions
6. Exercises
4. Chapter 11 Regression
1. 11.1 Least squares estimation
1. 11.1.1 Examples
2. 11.1.2 Method of least squares
3. 11.1.3 Linear regression
4. 11.1.4 Regression and correlation
5. 11.1.5 Overfitting a model
2. 11.2 Analysis of variance, prediction, and further inference
1. 11.2.1 ANOVA and R-square
2. 11.2.2 Tests and confidence intervals
3. 11.2.3 Prediction
3. 11.3 Multivariate regression
1. 11.3.1 Introduction and examples
2. 11.3.2 Matrix approach and least squares estimation
3. 11.3.3 Analysis of variance, tests, and prediction
4. 11.4 Model building
2. 11.4.2 Extra sum of squares, partial F-tests, and variable selection
3. 11.4.3 Categorical predictors and dummy variables
5. Summary and conclusions
6. Exercises
8. Part IV Appendix
1. Chapter 12 Appendix
1. 12.1 Inventory of distributions
2. 12.2 Distribution tables
3. 12.3 Calculus review
1. 12.3.1 Inverse function
2. 12.3.2 Limits and continuity
3. 12.3.3 Sequences and series
4. 12.3.4 Derivatives, minimum, and maximum
5. 12.3.5 Integrals
4. 12.4 Matrices and linear systems
5. 12.5 Answers to selected exercises