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Probability Models for Computer Science - Sheldon M. Ross

Probability Models for Computer Science


Published: 1st June 2001
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The role of probability in computer science has been growing for years and, in lieu of a tailored textbook, many courses have employed a variety of similar, but not entirely applicable, alternatives. To meet the needs of the computer science graduate student (and the advanced undergraduate), best-selling author Sheldon Ross has developed the premier probability text for aspiring computer scientists involved in computer simulation and modeling. The math is precise and easily understood. As with his other texts, Sheldon Ross presents very clear explanations of concepts and covers those probability models that are most in demand by, and applicable to, computer science and related majors and practitioners.
Many interesting examples and exercises have been chosen to illuminate the techniques presented
Examples relating to bin packing, sorting algorithms, the find algorithm, random graphs, self-organising list problems, the maximum weighted independent set problem, hashing, probabilistic verification, max SAT problem, queuing networks, distributed workload models, and many othersMany interesting examples and exercises have been chosen to illuminate the techniques presented

Prefacep. xi
Probabilityp. 1
Axioms of Probabilityp. 1
Conditional Probability and Independencep. 1
Random Variablesp. 2
Expected Value and Variancep. 5
Moment-Generating Functions and Laplace Transformsp. 17
Conditional Expectationp. 20
Exponential Random Variablesp. 32
Limit Theoremsp. 41
Exercisesp. 43
Some Examplesp. 49
A Random Graphp. 49
The Quicksort and Find Algorithmsp. 55
A Self-Organizing List Modelp. 61
Random Permutationsp. 62
Exercisesp. 71
Probability Bounds, Approximations, and Computationsp. 75
Tail Probability Inequalitiesp. 75
The Second Moment and the Conditional Expectation Inequalityp. 79
Probability Bounds via the Importance Sampling Identityp. 87
Poisson Random Variables and the Poisson Paradigmp. 89
Compound Poisson Random Variablesp. 94
Exercisesp. 100
Markov Chainsp. 103
Introductionp. 103
Chapman-Kolmogorov Equationsp. 105
Classification of Statesp. 106
Limiting and Stationary Probabilitiesp. 115
Some Applicationsp. 121
Time-Reversible Markov Chainsp. 131
Markov Chain Monte Carlo Methodsp. 142
Exercisesp. 147
The Probabilistic Methodp. 151
Introductionp. 151
Using Probability To Prove Existencep. 151
Obtaining Bounds from Expectationsp. 153
The Maximum Weighted Independent Set Problem: A Bound and a Random Algorithmp. 156
The Set-Covering Problemp. 161
Antichainsp. 163
The Lovasz Local Lemmap. 164
A Random Algorithm for Finding the Minimal Cut in a Graphp. 169
Exercisesp. 171
Martingalesp. 175
Definitions and Examplesp. 175
The Martingale Stopping Theoremp. 177
The Hoeffding-Azuma Inequalityp. 189
Submartingalesp. 192
Exercisesp. 194
Poisson Processesp. 199
The Nonstationary Poisson Processp. 199
The Stationary Poisson Processp. 203
Some Poisson Process Computationsp. 205
Classifying the Events of a Nonstationary Poisson Processp. 211
Conditional Distribution of the Arrival Timesp. 215
Exercisesp. 217
Queueing Theoryp. 221
Introductionp. 221
Preliminariesp. 222
Exponential Modelsp. 226
Birth-and-Death Exponential Queueing Systemsp. 230
The Backwards Approach in Exponential Queuesp. 238
A Closed Queueing Networkp. 239
An Open Queueing Networkp. 243
The M/G/1 Queuep. 248
Priority Queuesp. 255
Exercisesp. 258
Simulationp. 261
Monte Carlo Simulationp. 261
Generating Discrete Random Variablesp. 263
Generating Continuous Random Variables: The Inverse Transform Approachp. 266
The Rejection Methodp. 268
Variance Reductionp. 272
Exercisesp. 280
Referencesp. 283
Indexp. 285
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780125980517
ISBN-10: 0125980515
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 304
Published: 1st June 2001
Country of Publication: US
Dimensions (cm): 22.91 x 15.19  x 1.75
Weight (kg): 0.58