### Features

Leads students from standard probability and statistics topics to stochastic processes, queuing systems, and simulations techniques Describes the most commonly used types of distributions, including binomial, geometric, Poisson, uniform, exponential, gamma, and normal Introduces Monte Carlo methods to estimate probabilities, expectations, and other distribution characteristics Teaches how to estimate parameters of interest, test hypotheses, fit regression models, and make forecasts Provides Matlab computer codes for simulation and computation Contains many detailed examples and exercises that have direct applications to computer science and related fields Summarizes the main concepts at the end of each chapter and reviews calculus and linear algebra in the appendix Satisfies the Accreditation Board for Engineering and Technology (ABET) requirements for probability and statistics Includes a solutions manual with qualifying course adoptions
### Summary

In modern computer science, software engineering, and other fields, the need arises to make decisions under uncertainty. Presenting probability and statistical methods, simulation techniques, and modeling tools,

** Probability and Statistics for Computer Scientists** helps students solve problems and make optimal decisions in uncertain conditions, select stochastic models, compute probabilities and forecasts, and evaluate performance of computer systems and networks.

After introducing probability and distributions, this easy-to-follow textbook provides two course options. The first approach is a probability-oriented course that begins with stochastic processes, Markov chains, and queuing theory, followed by computer simulations and Monte Carlo methods. The second approach is a more standard, statistics-emphasized course that focuses on statistical inference, estimation, hypothesis testing, and regression. Assuming one or two semesters of college calculus, the book is illustrated throughout with numerous examples, exercises, figures, and tables that stress direct applications in computer science and software engineering. It also provides MATLAB^{®} codes and demonstrations written in simple commands that can be directly translated into other computer languages.

By the end of this course, advanced undergraduate and beginning graduate students should be able to read a word problem or a corporate report, realize the uncertainty involved in the described situation, select a suitable probability model, estimate and test its parameters based on real data, compute probabilities of interesting events and other vital characteristics, and make appropriate conclusions and forecasts.

### Table of Contents

**PREFACE**

**INTRODUCTION AND OVERVIEW**

Making decisions under uncertainty

Overview of this book

**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**

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

**INTRODUCTION TO STATISTICS**

Population and sample, parameters and statistics

Simple descriptive statistics

Graphical statistics

**STATISTICAL INFERENCE**

Parameter estimation

Confidence intervals

Unknown standard deviation

Hypothesis testing

Bayesian estimation and hypothesis testing

**REGRESSION**

Least squares estimation

Analysis of variance, prediction, and further inference

Multivariate regression

Model building

**APPENDIX**

Inventory of distributions

Distribution tables

Calculus review

Matrices and linear systems

Answers to selected exercises

**Index**
### Reviews

"… 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, Cal Poly State University, *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