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. 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
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.
