Probability and Statistics for Computer Scientists

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  • 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

    Making decisions under uncertainty
    Overview of this book
    Sample space, events, and probability
    Rules of probability
    Equally likely outcomes. Combinatorics
    Conditional probability. Independence
    Distribution of a random variable
    Distribution of a random vector
    Expectation and variance
    Families of discrete distributions
    Probability density
    Families of continuous distributions
    Central limit theorem
    Simulation of random variables
    Solving problems by Monte Carlo methods
    Definitions and classifications
    Markov processes and Markov chains
    Counting processes
    Simulation of stochastic processes
    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
    Population and sample, parameters and statistics
    Simple descriptive statistics
    Graphical statistics
    Parameter estimation
    Confidence intervals
    Unknown standard deviation
    Hypothesis testing
    Bayesian estimation and hypothesis testing
    Least squares estimation
    Analysis of variance, prediction, and further inference
    Multivariate regression
    Model building
    Inventory of distributions
    Distribution tables
    Calculus review
    Matrices and linear systems
    Answers to selected exercises

    Editorial 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