Probability and Statistics with Reliability, Queuing, and Computer Science Applications

by Trivedi, Kishor S.

• ISBN13: 9780471333418
• ISBN10: 0471333417
• Edition: 2nd
• Format: Hardcover
• Copyright: 2001-11-28
• Publisher: Wiley

Summary

An accessible introduction to probability, stochastic processes, and statistics for computer science and engineering applications This updated and revised edition of the popular classic 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 nets?as 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.

Author Biography

KISHOR S. TRIVEDI, PhD, is the Hudson Professor of Electrical and Computer Engineering at Duke University, Durham, North Carolina. His research interests include computer networks, fault-tolerant computing, modeling tools, and reliability modeling.

Table of Contents

Preface to the Second Edition	ix
Preface to the First Edition	xi
Acronyms	xiii
Introduction	1	(60)
Motivation	1	(1)
Probability Models	2	(1)
Sample Space	3	(3)
Events	6	(1)
Algebra of Events	7	(4)
Graphical Methods of Representing Events	11	(2)
Probability Axioms	13	(6)
Combinatorial Problems	19	(4)
Conditional Probability	23	(2)
Independence of Events	25	(13)
Bayes' Rule	38	(7)
Bernoulli Trials	45	(16)
Discrete Random Variables	61	(54)
Introduction	61	(1)
Random Variables and Their Event Spaces	62	(2)
The Probability Mass Function	64	(2)
Distribution Functions	66	(2)
Special Discrete Distributions	68	(24)
Analysis of Program MAX	92	(4)
The Probability Generating Function	96	(3)
Discrete Random Vectors	99	(5)
Independent Random Variables	104	(11)
Continuous Random Variables	115	(78)
Introduction	115	(4)
The Exponential Distribution	119	(5)
The Reliability and Failure Rate	124	(5)
Some Important Distributions	129	(19)
Functions of a Random Variable	148	(5)
Jointly Distributed Random Variables	153	(4)
Order Statistics	157	(10)
Distribution of Sums	167	(15)
Functions of Normal Random Variables	182	(11)
Expectation	193	(54)
Introduction	193	(4)
Moments	197	(3)
Expectation Based on Multiple Random Variables	200	(8)
Transform Methods	208	(9)
Moments and Transforms of Some Distributions	217	(11)
Computation of Mean Time to Failure	228	(9)
Inequalities and Limit Theorems	237	(10)
Conditional Distribution and Expectation	247	(42)
Introduction	247	(8)
Mixture Distributions	255	(7)
Conditional Expectation	262	(6)
Impefect Fault Coverage and Reliability	268	(11)
Random Sums	279	(10)
Stochastic Processes	289	(48)
Introduction	289	(5)
Classification of Stochastic Processes	294	(6)
The Bernoulli Process	300	(4)
The Poisson Process	304	(10)
Renewal Processes	314	(5)
Availability Analysis	319	(9)
Random Incidence	328	(4)
Renewal Model of Program Behavior	332	(5)
Discrete-Time Markov Chains	337	(68)
Introduction	337	(4)
Computation of n-step Transition Probabilities	341	(6)
State Classification and Limiting Probabilities	347	(9)
Distribution of Times Between State Changes	356	(2)
Markov Modulated Bernoulli Process	358	(3)
Irreducible Finite Chains with Aperiodic States	361	(16)
* The M/G/1 Queuing System	377	(8)
Discrete-Time Birth-Death Processes	385	(7)
Finite Markov Chains with Absorbing States	392	(13)
Continuous-Time Markov Chains	405	(150)
Introduction	405	(7)
The Birth-Death Process	412	(34)
Other Special Cases of the Birth-Death Model	446	(8)
Non-Birth-Death Processes	454	(42)
Markov Chains with Absorbing States	496	(24)
Solution Techniques	520	(10)
Automated Generation	530	(25)
Networks of Queues	555	(82)
Introduction	555	(5)
Open Queuing Networks	560	(8)
Closed Queuing Networks	568	(28)
General Service Distribution and Multiple Job Types	596	(8)
Non-product-form Networks	604	(13)
Computing Response Time Distribution	617	(13)
Summary	630	(7)
Statistical Inference	637	(90)
Introduction	637	(2)
Parameter Estimation	639	(53)
Hypothesis Testing	692	(35)
Regression and Analysis of Variance	727	(38)
Introduction	727	(5)
Least-squares Curve Fitting	732	(3)
The Coefficients of Determination	735	(3)
Confidence Intervals in Linear Regression	738	(4)
Trend Detection and Slope Estimation	742	(3)
Correlation Analysis	745	(3)
Simple Nonlinear Regression	748	(1)
Higher-dimensional Least-squares Fit	749	(2)
Analysis of Variance	751	(14)
A Bibliography	765	(12)
A.1 Theory	765	(5)
A.2 Applications	770	(7)
B Properties of Distributions	777	(3)
C Statistical Tables	780	(21)
D Laplace Transforms	801	(7)
E Program Performance Analysis	808	(3)
Author Index	811	(8)
Subject Index	819