Introduction to Probability Models 9th Edition by Sheldon Ross 0125980620 9780125980623
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Authors:Sheldon M. Ross , Series:Artificial Intelligence [39] , Tags:Artificial Intelligence; s; Probability & Statistics; General; Bayesian Analysis , Author sort:Ross, Sheldon M. , Ids:Google; 9780124079489 , Languages:Languages:eng , Published:Published:May 2014 , Publisher:Academic Press , Comments:Comments:Sheldon Ross’s classic bestseller, Introduction to Probability Models, has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It introduces elementary probability theory and stochastic processes, and shows how probability theory can be applied fields such as engineering, computer science, management science, the physical and social sciences, and operations research. The hallmark features of this renowned text remain in this eleventh edition: superior writing style; excellent exercises and examples covering the wide breadth of coverage of probability topic; and real-world applications in engineering, science, business and economics. The 65% new chapter material includes coverage of finite capacity queues, insurance risk models, and Markov chains, as well as updated data. Updated data, and a list of commonly used notations and equations, instructor’s solutions manualOffers new applications of probability models in biology and new material on Point Processes, including the Hawkes processIntroduces elementary probability theory and stochastic processes, and shows how probability theory can be applied in fields such as engineering, computer science, management science, the physical and social sciences, and operations researchCovers finite capacity queues, insurance risk models, and Markov chains Contains compulsory material for new Exam 3 of the Society of Actuaries including several sections in the new examsAppropriate for a full year course, this book is written under the assumption that students are familiar with calculus
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ISBN 10: 0125980620
ISBN 13: 9780125980623
Author: Sheldon M. Ross
A new section (3.7) on COMPOUND RANDOM VARIABLES, that can be used to establish a recursive formula for computing probability mass functions for a variety of common compounding distributions.
A new section (4.11) on HIDDDEN MARKOV CHAINS, including the forward and backward approaches for computing the joint probability mass function of the signals, as well as the Viterbi algorithm for determining the most likely sequence of states.
Simplified Approach for Analyzing Nonhomogeneous Poisson processes
Additional results on queues relating to the
(a) conditional distribution of the number found by an M/M/1 arrival who spends a time t in the system,;
(b) inspection paradox for M/M/1 queues
(c) M/G/1 queue with server breakdown
Many new examples and exercises.
Introduction to Probability Models 9th Table of contents:
1 Introduction to Probability Theory
1.1. Introduction
1.2. Sample Space and Events
1.3. Probabilities Defined on Events
1.4. Conditional Probabilities
1.5. Independent Events
1.6. Bayes’ Formula
Exercises
References
2 Random Variables
2.1. Random Variables
2.2. Discrete Random Variables
2.3. Continuous Random Variables
2.4. Expectation of a Random Variable
2.5. Jointly Distributed Random Variables
2.6. Moment Generating Functions
2.7. Limit Theorems
2.8. Stochastic Processes
Exercises
References
3 Conditional Probability and Conditional Expectation
3.1. Introduction
3.2. The Discrete Case
3.3. The Continuous Case
3.4. Computing Expectations by Conditioning
3.5. Computing Probabilities by Conditioning
3.6. Some Applications
3.7. An Identity for Compound Random Variables
Exercises
4 Markov Chains
4.1. Introduction
4.2. Chapman–Kolmogorov Equations
4.3. Classification of States
4.4. Limiting Probabilities
4.5. Some Applications
4.6. Mean Time Spent in Transient States
4.7. Branching Processes
4.8. Time Reversible Markov Chains
4.9. Markov Chain Monte Carlo Methods
4.10. Markov Decision Processes
4.11. Hidden Markov Chains
Exercises
References
5 The Exponential Distribution and the Poisson Process
5.1. Introduction
5.2. The Exponential Distribution
5.3. The Poisson Process
5.4. Generalizations of the Poisson Process
Exercises
References
6 Continuous-Time Markov Chains
6.1. Introduction
6.2. Continuous-Time Markov Chains
6.3. Birth and Death Processes
6.4. The Transition Probability Function
6.5. Limiting Probabilities
6.6. Time Reversibility
6.7. Uniformization
6.8. Computing the Transition Probabilities
Exercises
References
7 Renewal Theory and Its Applications
7.1. Introduction
7.2. Distribution of N(t)
7.3. Limit Theorems and Their Applications
7.4. Renewal Reward Processes
7.5. Regenerative Processes
7.6. Semi-Markov Processes
7.7. The Inspection Paradox
7.8. Computing the Renewal Function
7.9. Applications to Patterns
7.10. The Insurance Ruin Problem
Exercises
References
8 Queueing Theory
8.1. Introduction
8.2. Preliminaries
8.3. Exponential Models
8.4. Network of Queues
8.5. The System M/G/1
8.6. Variations on the M/G/1
8.7. The Model G/M/1
8.8. A Finite Source Model
8.9. Multiserver Queues
Exercises
References
9 Reliability Theory
9.1. Introduction
9.2. Structure Functions
9.3. Reliability of Systems of Independent Components
9.4. Bounds on the Reliability Function
9.5. System Life as a Function of Component Lives
9.6. Expected System Lifetime
9.7. Systems with Repair
Exercises
References
10 Brownian Motion and Stationary Processes
10.1. Brownian Motion
10.2. Hitting Times, Maximum Variable, and the Gambler’s Ruin Problem
10.3. Variations on Brownian Motion
10.4. Pricing Stock Options
10.5. White Noise
10.6. Gaussian Processes
10.7. Stationary and Weakly Stationary Processes
10.8. Harmonic Analysis of Weakly Stationary Processes
Exercises
References
11 Simulation
11.1. Introduction
11.2. General Techniques for Simulating Continuous Random Variables
11.3. Special Techniques for Simulating Continuous Random Variables
11.4. Simulating from Discrete Distributions
11.5. Stochastic Processes
11.6. Variance Reduction Techniques
11.7. Determining the Number of Runs
11.8. Coupling from the Past
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