Probability and statistics for computer scientists / Michael Baron.

Includes bibliographical references and index.

Introduction and Overviewp. 1 Making decisions under uncertaintyp. 1 Overview of this bookp. 3 Probabilityp. 9 Sample space, events, and probabilityp. 9 Rules of Probabilityp. 11 Equally likely outcomes. Combinatoricsp. 20 Conditional probability. Independencep. 28 Discrete Random Variables and their Distributionsp. 41 Distribution of a random variablep. 41 Distribution of a random vectorp. 46 Expectation and variancep. 49 Families of discrete distributionsp. 61 Continuous Distributionsp. 81 Probability densityp. 81 Families of continuous distributionsp. 86 Central Limit Theoremp. 100 Computer Simulations and Monte Carlo Methodsp. 111 Introductionp. 111 Simulation of random variablesp. 114 Solving problems by Monte Carlo methodsp. 126 Stochastic Processesp. 143 Definitions and Classificationsp. 143 Markov processes and Markov chainsp. 145 Counting processesp. 162 Simulation of stochastic processesp. 172 Queuing Systemsp. 183 Main components of a queuing systemp. 183 The Little's Lawp. 186 Bernoulli single-server queuing processp. 189 M/M/1 systemp. 195 Multiserver queuing systemsp. 202 Simulation of queuing systemsp. 212 Introduction to Statisticsp. 221 Population and sample, parameters and statisticsp. 222 Simple descriptive statisticsp. 224 Graphical statisticsp. 238 Statistical Inferencep. 253 Parameter estimationp. 253 Confidence intervalsp. 262 Unknown standard deviationp. 270 Hypothesis testingp. 282 Bayesian estimation and hypothesis testingp. 305 Regressionp. 327 Least squares estimationp. 327 Analysis of variance, prediction, and further inferencep. 335 Multivariate regressionp. 348 Model buildingp. 358 Appendixp. 371 Inventory of distributionsp. 371 Distribution tablesp. 377 Calculus reviewp. 391 Matrices and linear systemsp. 398 Answers to selected exercisesp. 404 Indexp. 409 Table of Contents provided by Ingram. All Rights Reserved.

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.

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