Introduction to Probability Models

by
Edition: 7th
Format: Hardcover
Pub. Date: 2000-02-01
Publisher(s): Academic Pr
List Price: $83.95

Rent Textbook

Select for Price
There was a problem. Please try again later.

New Textbook

We're Sorry
Sold Out

Used Textbook

We're Sorry
Sold Out

eTextbook

We're Sorry
Not Available

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Summary

The seventh edition of the successful Introduction to Probability Models introduces elementary probability theory and the stochastic processes and is particularly well-suited to those applying probability theory to the study of phenomena in engineering, management science, the physical and social sciences, and operations research. Skillfully organized, Introduction to Probability Models covers all essential topics. Sheldon Ross, a talented and prolific textbook author, distinguishes this carefully and substantially revised book by his effort to develop in students an intuitive, and therefore lasting, grasp of probability theory. The seventh edition includes many new examples and exercises, with the majority of the new exercises being less demanding of the student. In addition, the text introduces stochastic processes, stressing applications, in an easily understood manner. There is a comprehensive introduction to the applied models of probability that stresses intuition. Both students and professors will agree that this is the most solid and widely used text for probability theory. * Provides a detailed coverage of the Markov Chain Monte Carlo methods and Markov Chain covertimes * Gives a thorough presentation of k-record values and the surprising Ignatov's theorem * Includes examples relating to: "Random walks to circles," "The matching rounds problem," "The best prize problem" and many more * Contains a comprehensive appendix with the answers to approximately 100 exercises from throughout the text * Accompanied by a complete instructor's solutions manual with step-by-step solutions to all exercises NEW TO THIS EDITION * Includes many new and easier examples and exercises * Offers new material on utilizing probabilistic method in combinatorial optimization problems * Includes new material on suspended animation reliability models * Contains new material on random algorithms and cycles of random permutations

Table of Contents

Preface to the Fifth Edition xi
Preface to the Sixth Edition xiii
Preface to the Seventh Edition xv
Introduction to Probability Theory
1(22)
Introduction
1(1)
Sample Space and Events
1(3)
Probabilities Defined on Events
4(2)
Conditional Probabilities
6(4)
Independent Events
10(2)
Bayes' Formula
12(11)
Exercises
15(6)
References
21(2)
Random Variables
23(70)
Random Variables
23(4)
Discrete Random Variables
27(6)
The Bernoulli Random Variable
27(1)
The Binomial Random Variable
28(3)
The Geometric Random Variable
31(1)
The Poisson Random Variable
31(2)
Continuous Random Variables
33(4)
The Uniform Random Variable
34(1)
Exponential Random Variables
35(1)
Gamma Random Variables
35(1)
Normal Random Variables
36(1)
Expectation of a Random Variable
37(9)
The Discrete Case
37(3)
The Continuous Case
40(2)
Expectation of a Function of a Random Variable
42(4)
Jointly distributed Random Variables
46(16)
Joint Distribution Functions
46(4)
Independent Random Variables
50(1)
Covariance and Variance of Sums of Random Variables
51(8)
Joint Probability Distribution of Functions of Random Variables
59(3)
Moment Generating Functions
62(11)
The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population
70(3)
Limit Theorems
73(6)
Stochastic Processes
79(14)
Exercises
82(10)
References
92(1)
Conditional Probability and Conditional Expectation
93(70)
Introduction
93(1)
The Discrete Case
93(5)
The Continuous Case
98(3)
Computing Expectations by Conditioning
101(13)
Computing Probabilities by Conditioning
114(14)
Some Applications
128(35)
A List Model
128(1)
A Random Graph
129(8)
Uniform Priors, Polya's Urn Model, and Bose-Einstein Statistics
137(4)
The k-Record Values of Discrete Random Variables
141(4)
Exercises
145(18)
Markov Chains
163(78)
Introduction
163(3)
Chapman-Kolmogorov Equations
166(2)
Classification of States
168(10)
Limiting Probabilities
178(10)
Some Applications
188(12)
The Gambler's Ruin Problem
188(4)
A Model for Algorithmic Efficiency
192(2)
Using a Random Walk to analyze a Probabilistic Algorithm for the Satisfiability Problem
194(6)
Mean Time Spent in Transient States
200(2)
Branching Processes
202(3)
Time Reversible Markov Chains
205(11)
Markov Chain Monte Carlo Methods
216(6)
Markov Decision Processes
222(19)
Exercises
226(14)
References
240(1)
The Exponential distribution and the Poisson Process
241(72)
Introduction
241(1)
The Exponential Distribution
242(14)
Definition
242(1)
Properties of the exponential Distribution
243(5)
Further Properties of the Exponential Distribution
248(5)
Convolutions of Exponential Random Variables
253(3)
The Poisson Process
256(28)
Counting Processes
256(2)
Definition of the Poisson Process
258(3)
Interarrival and Waiting Time Distributions
261(3)
Further Properties of Poisson Processes
264(6)
Conditional Distribution of the Arrival Times
270(11)
Estimating software Reliability
281(3)
Generalizations of the Poisson Process
284(29)
Nonhomogeneous Poisson Process
284(5)
Compound Poisson Process
289(6)
Exercises
295(16)
References
311(2)
Continuous-Time Markov Chains
313(50)
Introduction
313(1)
Continuous-Time Markov Chains
314(2)
Birth and Death Processes
316(7)
The Transition Probability Function Pij(t)
323(8)
Limiting Probabilities
331(7)
Time Reversibility
338(8)
Uniformization
346(3)
Computing the Transition Probabilities
349(14)
Exercises
352(9)
References
361(2)
Renewal Theory and Its Applications
363(64)
Introduction
363(2)
Distribution of N(t)
365(3)
Limit Theorems and Their Applications
368(9)
Renewal Reward Processes
377(9)
Regenerative Processes
386(9)
Alternating Renewal Processes
389(6)
Semi-Markov Processes
395(3)
The Inspection Paradox
398(2)
Computing the Renewal Function
400(3)
Applications to Patterns
403(24)
Patterns of Discrete Random Variables
404(6)
The Expected Time to a Maximal Run of distinct Values
410(2)
Increasing runs of Continuous Random Variables
412(1)
Exercises
413(12)
References
425(2)
Queueing Theory
427(72)
Introduction
427(1)
Preliminaries
428(4)
Cost Equations
429(1)
Steady-State Probabilities
430(2)
Exponential Models
432(15)
A Single-Server Exponential Queueing System
432(6)
A Single-Server Exponential Queueing System Having Finite Capacity
438(4)
A Shoeshine Shop
442(2)
A Queueing System with Bulk Service
444(3)
Network of Queues
447(11)
Open Systems
447(5)
Closed Systems
452(6)
The System M/G/1
458(3)
Preliminaries: Work and Another Cost Identity
458(1)
Application of Work to M/G/1
459(1)
Busy Periods
460(1)
Variations on the M/G/1
461(9)
The M/G/1 with Random-Sized Batch Arrivals
461(2)
Priority Queues
463(3)
An M/G/1 Optimization Example
466(4)
The Model G/M/1
470(5)
The G/M/1 Busy and Idle Periods
475(1)
A Finite Source Model
475(4)
Multiserver Queues
479(20)
Erlang's Loss System
479(2)
The M/M/k Queue
481(1)
The G/M/k Queue
481(2)
The M/G/k Queue
483(1)
Exercises
484(12)
References
496(3)
Reliability Theory
499(50)
Introduction
499(1)
Structure Functions
500(6)
Minimal Path and Minimal Cut Sets
502(4)
Reliability of Systems of Independent Components
506(4)
Bounds on the Reliability Function
510(11)
Method of Inclusion and Exclusion
511(8)
Second Method for Obtaining Bounds on r(p)
519(2)
System Life as a Function of Component Lives
521(8)
Expected System Lifetime
529(6)
An Upper Bound on the Expected Life of a Parallel System
533(2)
Systems with Repair
535(14)
A Series Model with Suspended Animation
539(3)
Exercises
542(6)
References
548(1)
Brownian Motion and Stationary Processes
549(36)
Brownian Motion
549(4)
Hitting Times, Maximum Variable, and the Gambler's Ruin Problem
553(1)
Variations on Brownian Motion
554(2)
Brownian Motion with Drift
554(1)
Geometric Brownian Motion
555(1)
Pricing Stock Options
556(11)
An Example in Options Pricing
556(2)
The Arbitrage Theorem
558(3)
The Black - Scholes Option Pricing Formula
561(6)
White Noise
567(2)
Gaussian Processes
569(3)
Stationary and Weakly Stationary Processes
572(5)
Harmonic Analysis of Weakly Stationary Processes
577(8)
Exercises
579(5)
References
584(1)
Simulation
585(64)
Introduction
585(5)
General Techniques for Simulating Continuous Random Variables
590(8)
The Inverse Transformation Method
590(1)
The Rejection Method
591(4)
The Hazard Rate Method
595(3)
Special Techniques for Simulating Continuous Random Variables
598(8)
The Normal Distribution
598(4)
The Gamma Distribution
602(1)
The Chi-Squared Distribution
602(1)
The Beta (n, m) Distribution
603(1)
The Exponential Distribution--The von Neumann Algorithm
604(2)
Simulating from Discrete Distributions
606(7)
The Alias Method
610(3)
Stochastic Processes
613(11)
Simulating a Nonhomogeneous Poisson Process
615(6)
Simulating a Two-Dimensional Poisson Process
621(3)
Variance Reduction Techniques
624(15)
Use of Antithetic Variables
625(4)
Variance Reduction by Conditioning
629(4)
Control Variates
633(1)
Importance Sampling
634(5)
Determining the Number of Runs
639(10)
Exercises
640(8)
References
648(1)
Appendix: Solutions to Starred Exercises 649(38)
Index 687

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.