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# Probability and Statistics for Computer Scientists

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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.

## Table of Contents

**Introduction and Overview **Making decisions under uncertainty

Overview of this book

**Probability and Random Variables****Probability **Sample space, events, and probability

Rules of Probability

Equally likely outcomes. Combinatorics

Conditional probability. Independence

**Discrete Random Variables and Their Distributions**

Distribution of a random variable

Distribution of a random vector

Expectation and variance

Families of discrete distributions

**Continuous Distributions**

Probability density

Families of continuous distributions

Central limit theorem

**Computer Simulations and Monte Carlo Methods **Introduction

Simulation of random variables

Solving problems by Monte Carlo methods

**Stochastic Processes****Stochastic Processes **Definitions and classifications

Markov processes and Markov chains

Counting processes

Simulation of stochastic processes

**Queuing Systems**

Main components of a queuing system

The Little’s Law

Bernoulli single-server queuing process

M/M/1 system

Multiserver queuing systems

Simulation of queuing systems

**Statistics****Introduction to Statistics **Population and sample, parameters and statistics

Simple descriptive statistics

Graphical statistics

**Statistical Inference I**

Parameter estimation

Confidence intervals

Unknown standard deviation

Hypothesis testing

Inference about variances

**Statistical Inference II **Chi-square tests

Nonparametric statistics

Bootstrap

Bayesian inference

**Regression **Least squares estimation

Analysis of variance, prediction, and further inference

Multivariate regression

Model building

*Appendix *Appendix

Inventory of distributions

Distribution tables

Calculus review

Matrices and linear systems

Answers to selected exercises

Index

Summary, Conclusions, and Exercises are included at the end of each chapter.

## Author(s)

### Biography

**Michael Baron** is a professor of statistics at the University of Texas at Dallas. 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.

## Reviews

"… an immensely readable text intended for junior undergraduate to beginning graduate students in computer-related fields, though it could be suitable for any calculus-based probability and/or mathematical statistics course. … the book is well written, and very well suited to the target audience—individuals in computer-related fields. Through examples and exercises, the author does an excellent job demonstrating how probability and statistics are used in computer-related fields. The text could also be used for a standalone probability course or a two-semester probability and mathematical statistics sequence for mathematics and statistics students."

—The American Statistician, February 2015"The author has done his homework on the statistical tools needed for the particular challenges computer scientists encounter in statistics. Since the author has taken great care to select examples that are interesting and practical for computer scientists, the book should hold special appeal for that group. ... The content is illustrated with numerous figures, and concludes with appendices and an index. The book is erudite and demands a reader with a firm background in calculus. It could work well as a required text for an advanced undergraduate or graduate course."

—James Van Speybroeck,Computing Reviews, January 2014

Praise for the First Edition:"… students of all majors will benefit from the author’s fine presentation of applied probability models and computer simulation. I am seriously considering adopting it for a [probability-oriented course] … the chapters on simulation and applied probability models are truly outstanding …"

—Matthew A. Carlton,The American Statistician, August 2008“…well-organized text seems designed as a gentle introduction to the mathematics of probability and statistics. …helpful diagrams…surprisingly detailed.”

—John Maindonald,International Statistical Review, Vol. 75, No. 2, 2007"… an ideal textbook for computer science students. … This book is primarily intended for junior undergraduate to beginning graduate level students majoring in computer-related fields. It can also be used by electrical engineering, mathematics, statistics, actuarial science, and other majors for a standard introductory statistics course. Graduate students can use this book to prepare for probability-based courses such as queuing theory, artificial neural networks, and computer performance. Overall, this well-written text can be used as a standard reference on probability and statistical methods, simulation and modeling tools."

—Journal of the Royal Statistical Society"The book represents a good reference to all who are interested in statistics, modeling stochastic processes, and computer simulation. … The book’s material is invaluable and presented with clarity …"

—Journal of Applied Statistics, 2007