Probability and Statistics for Computer Scientists

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