Probability and Statistics for Computer Scientists, Second Edition

ISBN-10: 1439875901
ISBN-13: 9781439875902
Edition: 2nd 2013 (Revised)
Authors: Michael Baron
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Description: 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  More...

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Book details

Edition: 2nd
Copyright year: 2013
Publisher: Taylor & Francis Group
Publication date: 9/12/2013
Binding: Hardcover
Pages: 473
Size: 7.25" wide x 10.50" long x 1.25" tall
Weight: 2.508
Language: English

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 Scientistshelps 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#xAE;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.

List of Figures
List of Tables
Preface
Introduction and Overview
Making decisions under uncertainty
Overview of this book
Summary and conclusions
Exercises
Probability and Random Variables
Probability
Events and their probabilities
Outcomes, events, and the sample space
Set operations
Rules of Probability
Axioms of Probability
Computing probabilities of events
Applications in reliability
Combinatorics
Equally likely outcomes
Permutations and combinations
Conditional probability and independence
Summary and conclusions
Exercises
Discrete Random Variables and Their Distributions
Distribution of a random variable
Main concepts
Types of random variables
Distribution of a random vector
Joint distribution and marginal distributions
Independence of random variables
Expectation and variance
Expectation
Expectation of a function
Properties
Variance and standard deviation
Covariance and correlation
Properties
Chebyshev's inequality
Application to finance
Families of discrete distributions
Bernoulli distribution
Binomial distribution
Geometric distribution
Negative Binomial distribution
Poisson distribution
Poisson approximation of Binomial distribution
Summary and conclusions
Exercises
Continuous Distributions
Probability density
Families of continuous distributions
Uniform distribution
Exponential distribution
Gamma distribution
Normal distribution
Central Limit Theorem
Summary and conclusions
Exercises
Computer Simulations and Monte Carlo Methods
Introduction
Applications and examples
Simulation of random variables
Random number generators
Discrete methods
Inverse transform method
Rejection method
Generation of random vectors
Special methods
Solving problems by Monte Carlo methods
Estimating probabilities
Estimating means and standard deviations
Forecasting
Estimating lengths, areas, and volumes
Monte Carlo integration
Summary and conclusions
Exercises
II Stochastic Processes
Stochastic Processes
Definitions and classifications
Markov processes and Markov chains
Markov chains
Matrix approach
Steady-state distribution
Counting processes
Binomial process
Poisson process
Simulation of stochastic processes
Summary and conclusions
Exercises
Queuing Systems
Main components of a queuing system
The Little's Law
Bernoulli single-server queuing process
Systems with limited capacity
M/M/1 system
Evaluating the system's performance
Multiserver queuing systems
Bernoulli k-server queuing process
M/M/k systems
Unlimited number of servers and M/M/∞
Simulation of queuing systems
Summary and conclusions
Exercises
III Statistics
Introduction to Statistics
Population and sample, parameters and statistics
Simple descriptive statistics
Mean
Median
Quantiles, percentiles, and quartiles
Variance and standard deviation
Standard errors of estimates
Interquartile range
Graphical statistics
Histogram
Stem-and-leaf plot
Boxplot
Scatter plots and time plots
Summary and conclusions
Exercises
Statistical Inference I
Parameter estimation
Method of moments
Method of maximum likelihood
Estimation of standard errors
Confidence intervals
Construction of confidence intervals: a general method
Confidence interval for the population mean
Confidence interval for the difference between two means
Selection of a sample size
Estimating means with a given precision
Unknown standard deviation
Large samples
Confidence intervals for proportions
Estimating proportions with a given precision
Small samples: Student's t distribution
Comparison of two populations with unknown variances
Hypothesis testing
Hypothesis and alternative
Type I and Type II errors: level of significance
Level a tests: general approach
Rejection regions and power
Standard Normal null distribution (Z-test)
Z-tests for means and proportions
Pooled sample proportion
Unknown �: T-tests
Duality: two-sided tests and two-sided confidence intervals
P-value
Inference about variances
Variance estimator and Chi-square distribution
Confidence interval for the population variance
Testing variance
Comparison of two variances. F-distribution
Confidence interval for the ratio of population variances
F-tests comparing two variances
Summary and conclusions
Exercises
Statistical Inference II
Chi-square tests
Testing a distribution
Testing a family of distributions
Testing independence
Nonparametric statistics
Sign test
Wilcoxon signed rank test
Mann-Whitney-Wilcoxon rank sum test
Bootstrap
Bootstrap distribution and all bootstrap samples
Computer generated bootstrap samples
Bootstrap confidence intervals
Bayesian inference
Prior and posterior
Bayesian estimation
Bayesian credible sets
Bayesian hypothesis testing
Summary and conclusions
Exercises
Regression
Least squares estimation
Examples
Method of least squares
Linear regression
Regression and correlation
Overfitting a model
Analysis of variance, prediction, and further inference
ANOVA and R-square
Tests and confidence intervals
Prediction
Multivariate regression
Introduction and examples
Matrix approach and least squares estimation
Analysis of variance, tests, and prediction
Model building
Adjusted R-square
Extra sum of squares, partial F-tests, and variable selection
Categorical predictors and dummy variables
Summary and conclusions
Exercises
IV Appendix
Appendix
Inventory of distributions
Discrete families
Continuous families
Distribution tables
Calculus review
Inverse function
Limits and continuity
Sequences and series
Derivatives, minimum, and maximum
Integrals
Matrices and linear systems
Answers to selected exercises
Index

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