Probability and Statistics for Computer Scientists, Second Edition

Name: Probability and Statistics for Computer Scientists, Second Edition
Price: 12.46 USD
Availability: InStock
ISBN: 9781439875902

ISBN-10: 1439875901

ISBN-13: 9781439875902

Edition: 2nd 2013 (Revised)

Authors: Michael Baron

List price: $63.99

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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 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,…

Book details

List price: $63.99
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: 2.244
Language: English



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 ï¿½: 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