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E-raamat: Probability and Statistics with Reliability, Queuing, and Computer Science Applications

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(Duke University, Durham, North Carolina)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 11-Jul-2016
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9780471460817
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Probability and Statistics with Reliability, Queuing, and Computer Science ApplicationsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 11-Jul-2016
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9780471460817
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An accessible introduction to probability, stochastic processes, and statistics for computer science and engineering applications

Second edition now also available in Paperback. This updated and revised edition of the popular classic first edition relates fundamental concepts in probability and statistics to the computer sciences and engineering. The author uses Markov chains and other statistical tools to illustrate processes in reliability of computer systems and networks, fault tolerance, and performance.

This edition features an entirely new section on stochastic Petri netsas well as new sections on system availability modeling, wireless system modeling, numerical solution techniques for Markov chains, and software reliability modeling, among other subjects. Extensive revisions take new developments in solution techniques and applications into account and bring this work totally up to date. It includes more than 200 worked examples and self-study exercises for each section.

Probability and Statistics with Reliability, Queuing and Computer Science Applications, Second Edition offers a comprehensive introduction to probability, stochastic processes, and statistics for students of computer science, electrical and computer engineering, and applied mathematics. Its wealth of practical examples and up-to-date information makes it an excellent resource for practitioners as well. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Arvustused

"The book offers a comprehensive introduction to probability, stochastic processes, and statistics for students of computer science, electrical and computer engineering, and applied mathematics. Its wealth of practical examples and up-to-date information makes it an excellent resource for practitioners as well." (Zentralblatt MATH, 2016)

"I highly recommend this book for academics for use as a textbook and for researchers and professionals in the field as a useful reference." (Interfaces, September/ October 2004)

"This introduction...uses Markov chains and other statistical tools to illustrate process in reliability of computer systems, fault tolerance, and performance." (SciTech Book News, Vol. 26, No. 2, June 2002)

"...an excellent self-contained book.... I recommend the book to beginners and veterans in the field..." (Computer Journal, Vol.45, No.6, 2002)

"This book is a tour de force of clear, virtually error-free exposition of probability as it is applied in a host of up-to-date contexts.... It will richly reward the...reader.... Read this book cover to cover. Its worth the effort." (Technometrics, Vol. 45, No. 1, February 2003)

Preface to the Paperback Edition ix
Preface to the Second Edition xi
Preface to the First Edition xiii
Acronyms xv
About the Companion Website xix
1 Introduction
1(64)
1.1 Motivation
1(1)
1.2 Probability Models
2(1)
1.3 Sample Space
3(3)
1.4 Events
6(1)
1.5 Algebra of Events
7(4)
1.6 Graphical Methods of Representing Events
11(2)
1.7 Probability Axioms
13(6)
1.8 Combinatorial Problems
19(5)
1.9 Conditional Probability
24(2)
1.10 Independence of Events
26(12)
1.11 Bayes' Rule
38(9)
1.12 Bernoulli Trials
47(18)
2 Discrete Random Variables
65(56)
2.1 Introduction
65(1)
2.2 Random Variables and Their Event Spaces
66(2)
2.3 The Probability Mass Function
68(2)
2.4 Distribution Functions
70(2)
2.5 Special Discrete Distributions
72(25)
2.6 Analysis of Program MAX
97(4)
2.7 The Probability Generating Function
101(3)
2.8 Discrete Random Vectors
104(6)
2.9 Independent Random Variables
110(11)
3 Continuous Random Variables
121(80)
3.1 Introduction
121(4)
3.2 The Exponential Distribution
125(5)
3.3 The Reliability and Failure Rate
130(5)
3.4 Some Important Distributions
135(19)
3.5 Functions of a Random Variable
154(5)
3.6 Jointly Distributed Random Variables
159(4)
3.7 Order Statistics
163(11)
3.8 Distribution of Sums
174(16)
3.9 Functions of Normal Random Variables
190(11)
4 Expectation
201(56)
4.1 Introduction
201(4)
4.2 Moments
205(4)
4.3 Expectation Based on Multiple Random Variables
209(7)
4.4 Transform Methods
216(10)
4.5 Moments and Transforms of Some Distributions
226(12)
4.6 Computation of Mean Time to Failure
238(9)
4.7 Inequalities and Limit Theorems
247(10)
5 Conditional Distribution and Expectation
257(44)
5.1 Introduction
257(9)
5.2 Mixture Distributions
266(7)
5.3 Conditional Expectation
273(7)
5.4 Imperfect Fault Coverage and Reliability
280(10)
5.5 Random Sums
290(11)
6 Stochastic Processes
301(50)
6.1 Introduction
301(6)
6.2 Classification of Stochastic Processes
307(6)
6.3 The Bernoulli Process
313(4)
6.4 The Poisson Process
317(10)
6.5 Renewal Processes
327(5)
6.6 Availability Analysis
332(10)
6.7 Random Incidence
342(4)
6.8 Renewal Model of Program Behavior
346(5)
7 Discrete-Time Markov Chains
351(70)
7.1 Introduction
351(5)
7.2 Computation of n-step Transition Probabilities
356(6)
7.3 State Classification and Limiting Probabilities
362(9)
7.4 Distribution of Times Between State Changes
371(2)
7.5 Markov Modulated Bernoulli Process
373(3)
7.6 Irreducible Finite Chains with Aperiodic States
376(15)
7.7 * The M/G/ 1 Queuing System
391(9)
7.8 Discrete-Time Birth-Death Processes
400(7)
7.9 Finite Markov Chains with Absorbing States
407(14)
8 Continuous-Time Markov Chains
421(156)
8.1 Introduction
421(7)
8.2 The Birth-Death Process
428(37)
8.3 Other Special Cases of the Birth-Death Model
465(9)
8.4 Non-Birth-Death Processes
474(45)
8.5 Markov Chains with Absorbing States
519(22)
8.6 Solution Techniques
541(11)
8.7 Automated Generation
552(25)
9 Networks of Queues
577(84)
9.1 Introduction
577(5)
9.2 Open Queuing Networks
582(8)
9.3 Closed Queuing Networks
590(30)
9.4 General Service Distribution and Multiple Job Types
620(8)
9.5 Non-product-form Networks
628(13)
9.6 Computing Response Time Distribution
641(13)
9.7 Summary
654(7)
10 Statistical Inference
661(92)
10.1 Introduction
661(2)
10.2 Parameter Estimation
663(55)
10.3 Hypothesis Testing
718(35)
11 Regression and Analysis of Variance
753(84)
11.1 Introduction
753(5)
11.2 Least-squares Curve Fitting
758(4)
11.3 The Coefficients of Determination
762(3)
11.4 Confidence Intervals in Linear Regression
765(3)
11.5 Trend Detection and Slope Estimation
768(3)
11.6 Correlation Analysis
771(3)
11.7 Simple Nonlinear Regression
774(1)
11.8 Higher-dimensional Least-squares Fit
775(3)
11.9 Analysis of Variance
778(13)
A Bibliography
791(13)
A.1 Theory
791(5)
A.2 Applications
796(8)
B Properties of Distributions
804(3)
C Statistical Tables
807(21)
D Laplace Transforms
828(7)
E Program Performance Analysis
835(2)
Author Index 837(8)
Subject Index 845
Kishor S. Trivedi, PhD, is the Hudson Professor of Electrical and Computer Engineering at Duke University, Durham, North Carolina. His research interests are in reliability and performance assessment of computer and communication systems. Dr. Trivedi has published extensively in these fields, with more than 600 articles and three books to his name. Dr. Trivedi is a Fellow of the IEEE and a Golden Core Member of the IEEE Computer Society.
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