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.
INTRODUCTION AND OVERVIEW
Making decisions under uncertainty
Overview of this book
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
Families of continuous distributions
Central limit theorem
COMPUTER SIMULATIONS AND MONTE CARLO METHODS
Simulation of random variables
Solving problems by Monte Carlo methods
Definitions and classifications
Markov processes and Markov chains
Simulation of stochastic processes
Main components of a queuing system
The Little’s Law
Bernoulli single-server queuing process
Multiserver queuing systems
Simulation of queuing systems
INTRODUCTION TO STATISTICS
Population and sample, parameters and statistics
Simple descriptive statistics
Unknown standard deviation
Bayesian estimation and hypothesis testing
Least squares estimation
Analysis of variance, prediction, and further inference
Inventory of distributions
Matrices and linear systems
Answers to selected exercises
"… 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