Introduction to Probability Models

ISBN-10: 0123756863
ISBN-13: 9780123756862
Edition: 10th 2010
Authors: Sheldon M. Ross
List price: $60.99
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Book details

List price: $60.99
Edition: 10th
Copyright year: 2010
Publisher: Elsevier Science & Technology
Publication date: 12/11/2009
Binding: Hardcover
Pages: 800
Size: 6.00" wide x 9.00" long x 1.25" tall
Weight: 1.672
Language: English

Preface
Introduction to Probability Theory
Introduction
Sample Space and Events
Probabilities Defined on Events
Conditional Probabilities
Independent Events
Bayes' Formula
Exercises
References
Random Variables
Random Variables
Discrete Random Variables
The Bernoulli Random Variable
The Binomial Random Variable
The Geometric Random Variable
The Poisson Random Variable
Continuous Random Variables
The Uniform Random Variable
Exponential Random Variables
Gamma Random Variables
Normal Random Variables
Expectation of a Random Variable
The Discrete Case
The Continuous Case
Expectation of a Function of a Random Variable
Jointly Distributed Random Variables
Joint Distribution Functions
Independent Random Variables
Covariance and Variance of Sums of Random Variables
Joint Probability Distribution of Functions of Random Variables
Moment Generating Functions
The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population
The Distribution of the Number of Events that Occur
Limit Theorems
Stochastic Processes
Exercises
References
Conditional Probability and Conditional Expectation
Introduction
The Discrete Case
The Continuous Case
Computing Expectations by Conditioning
Computing Variances by Conditioning
Computing Probabilities by Conditioning
Some Applications
A List Model
A Random Graph
Uniform Priors, Polya's Urn Model, and Bose-Einstein Statistics
Mean Time for Patterns
The k-Record Values of Discrete Random Variables
Left Skip Free Random Walks
An Identity for Compound Random Variables
Poisson Compounding Distribution
Binomial Compounding Distribution
A Compounding Distribution Related to the Negative Binomial
Exercises
Markov Chains
Introduction
Chapman-Kolmogorov Equations
Classification of States
Limiting Probabilities
Some Applications
The Gambler's Ruin Problem
A Model for Algorithmic Efficiency
Using a Random Walk to Analyze a Probabilistic Algorithm for the Satisfiability Problem
Mean Time Spent in Transient States
Branching Processes
Time Reversible Markov Chains
Markov Chain Monte Carlo Methods
Markov Decision Processes
Hidden Markov Chains
Predicting the States
Exercises
References
The Exponential Distribution and the Poisson Process
Introduction
The Exponential Distribution
Definition
Properties of the Exponential Distribution
Further Properties of the Exponential Distribution
Convolutions of Exponential Random Variables
The Poisson Process
Counting Processes
Definition of the Poisson Process
Interarrival and Waiting Time Distributions
Further Properties of Poisson Processes
Conditional Distribution of the Arrival Times
Estimating Software Reliability
Generalizations of the Poisson Process
Nonhomogeneous Poisson Process
Compound Poisson Process
Conditional or Mixed Poisson Processes
Exercises
References
Continuous-Time Markov Chains
Introduction
Continuous-Time Markov Chains
Birth and Death Processes
The Transition Probability Function P<sub>ij</sub>(t)
Limiting Probabilities
Time Reversibility
Uniformization
Computing the Transition Probabilities
Exercises
References
Renewal Theory and Its Applications
Introduction
Distribution of N(t)
Limit Theorems and Their Applications
Renewal Reward Processes
Regenerative Processes
Alternating Renewal Processes
Semi-Markov Processes
The Inspection Paradox
Computing the Renewal Function
Applications to Patterns
Patterns of Discrete Random Variables
The Expected Time to a Maximal Run of Distinct Values
Increasing Runs of Continuous Random Variables
The Insurance Ruin Problem
Exercises
References
Queueing Theory
Introduction
Preliminaries
Cost Equations
Steady-State Probabilities
Exponential Models
A Single-Server Exponential Queueing System
A Single-Server Exponential Queueing System Having Finite Capacity
Birth and Death Queueing Models
A Shoe Shine Shop
A Queueing System with Bulk Service
Network of Queues
Open Systems
Closed Systems
The System M/G/1
Preliminaries: Work and Another Cost Identity
Application of Work to M/G/1
Busy Periods
Variations on the M/G/1
The M/G/1 with Random-Sized Batch Arrivals
Priority Queues
An M/G/1 Optimization Example
The M/G/1 Queue with Server Breakdown
The Model G/M/1
The G/M/1 Busy and Idle Periods
A Finite Source Model
Multiserver Queues
Erlang's Loss System
The M/M/k Queue
The G/M/k Queue
The M/G/k Queue
Exercises
References
Reliability Theory
Introduction
Structure Functions
Minimal Path and Minimal Cut Sets
Reliability of Systems of Independent Components
Bounds on the Reliability Function
Method of Inclusion and Exclusion
Second Method for Obtaining Bounds on r(p)
System Life as a Function of Component Lives
Expected System Lifetime
An Upper Bound on the Expected Life of a Parallel System
Systems with Repair
A Series Model with Suspended Animation
Exercises
References
Brownian Motion and Stationary Processes
Brownian Motion
Hitting Times, Maximum Variable, and the Gambler's Ruin Problem
Variations on Brownian Motion
Brownian Motion with Drift
Geometric Brownian Motion
Pricing Stock Options
An Example in Options Pricing
The Arbitrage Theorem
The Black-Scholes Option Pricing Formula
White Noise
Gaussian Processes
Stationary and Weakly Stationary Processes
Harmonic Analysis of Weakly Stationary Processes
Exercises
References
Simulation
Introduction
General Techniques for Simulating Continuous Random Variables
The Inverse Transformation Method
The Rejection Method
The Hazard Rate Method
Special Techniques for Simulating Continuous Random Variables
The Normal Distribution
The Gamma Distribution
The Chi-Squared Distribution
The Beta (n, m) Distribution
The Exponential Distribution-The Von Neumann Algorithm
Simulating from Discrete Distributions
The Alias Method
Stochastic Processes
Simulating a Nonhomogeneous Poisson Process
Simulating a Two-Dimensional Poisson Process
Variance Reduction Techniques
Use of Antithetic Variables
Variance Reduction by Conditioning
Control Variates
Importance Sampling
Determining the Number of Runs
Generating from the Stationary Distribution of a Markov Chain
Coupling from the Past
Another Approach
Exercises
References
Appendix: Solutions to Starred Exercises
Index

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