Introduction to Probability Models,9780125980555

Introduction to Probability Models

by
Edition: 8th
ISBN13: 9780125980555
ISBN10: 0125980558
Format: Audio CD
Pub. Date: 2002-12-20
Publisher(s): Elsevier Science & Technology
List Price: $89.95

Buy Used

Usually Ships in 24-48 Hours
$67.46
Add to Cart

Rent Textbook

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

New Textbook

We're Sorry
Sold Out

eTextbook

We're Sorry
Not Available

Buy from our Marketplace starting at $3.25

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

Rosss classic bestseller has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries.

Table of Contents

Preface xiii
Introduction to Probability Theory
1(22)
Introduction
1(1)
Sample Space and Events
1(3)
Probabilities Defined on Events
4(3)
Conditional Probabilities
7(3)
Independent Events
10(2)
Bayes' Formula
12(11)
Exercises
15(6)
References
21(2)
Random Variables
23(74)
Random Variables
23(4)
Discrete Random Variables
27(7)
The Bernoulli Random Variable
28(1)
The Binomial Random Variable
29(2)
The Geometric Random Variable
31(1)
The Poisson Random Variable
32(2)
Continuous Random Variables
34(4)
The Uniform Random Variable
35(1)
Exponential Random Variables
36(1)
Gamma Random Variables
37(1)
Normal Random Variables
37(1)
Expectation of a Random Variable
38(9)
The Discrete Case
38(3)
The Continuous Case
41(2)
Expectation of a Function of a Random Variable
43(4)
Jointly Distributed Random Variables
47(17)
Joint Distribution Functions
47(4)
Independent Random Variables
51(2)
Covariance and Variance of Sums of Random Variables
53(8)
Joint Probability Distribution of Functions of Random Variables
61(3)
Moment Generating Functions
64(13)
The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population
74(3)
Limit Theorems
77(6)
Stochastic Processes
83(14)
Exercises
85(11)
References
96(1)
Conditional Probability and Conditional Expectation
97(84)
Introduction
97(1)
The Discrete Case
97(5)
The Continuous Case
102(3)
Computing Expectations by Conditioning
105(14)
Computing Variances by Conditioning
116(3)
Computing Probabilities by Conditioning
119(17)
Some Applications
136(45)
A List Model
136(2)
A Random Graph
138(8)
Uniform Priors, Polya's Urn Model, and Bose-Einstein Statistics
146(4)
Mean Time for Patterns
150(4)
A Compound Poisson Identity
154(4)
The k-Record Values of Discrete Random Variables
158(3)
Exercises
161(20)
Markov Chains
181(88)
Introduction
181(4)
Chapman--Kolmogorov Equations
185(4)
Classification of States
189(11)
Limiting Probabilities
200(13)
Some Applications
213(13)
The Gambler's Ruin Problem
213(4)
A Model for Algorithmic Efficiency
217(3)
Using a Random Walk to Analyze a Probabilistic Algorithm for the Satisfiability Problem
220(6)
Mean Time Spent in Transient States
226(2)
Branching Processes
228(4)
Time Reversible Markov Chains
232(11)
Markov Chain Monte Carlo Methods
243(5)
Markov Decision Processes
248(21)
Exercises
252(16)
References
268(1)
The Exponential Distribution and the Poisson Process
269(80)
Introduction
269(1)
The Exponential Distribution
270(18)
Definition
270(2)
Properties of the Exponential Distribution
272(7)
Further Properties of the Exponential Distribution
279(5)
Convolutions of Exponential Random Variables
284(4)
The Poisson Process
288(28)
Counting Processes
288(1)
Definition of the Poisson Process
289(4)
Interarrival and Waiting Time Distributions
293(2)
Further Properties of Poisson Processes
295(6)
Conditional Distribution of the Arrival Times
301(12)
Estimating Software Reliability
313(3)
Generalizations of the Poisson Process
316(33)
Nonhomogeneous Poisson Process
316(5)
Compound Poisson Process
321(6)
Conditional or Mixed Poisson Processes
327(3)
Exercises
330(18)
References
348(1)
Continuous-Time Markov Chains
349(52)
Introduction
349(1)
Continuous-Time Markov Chains
350(2)
Birth and Death Processes
352(7)
The Transition Probability Function Pij(t)
359(9)
Limiting Probabilities
368(8)
Time Reversibility
376(8)
Uniformization
384(4)
Computing the Transition Probabilities
388(13)
Exercises
390(9)
References
399(2)
Renewal Theory and Its Applications
401(74)
Introduction
401(2)
Distribution of N(t)
403(4)
Limit Theorems and Their Applications
407(9)
Renewal Reward Processes
416(9)
Regenerative Processes
425(9)
Alternating Renewal Processes
428(6)
Semi-Markov Processes
434(3)
The Inspection Paradox
437(3)
Computing the Renewal Function
440(3)
Applications to Patterns
443(12)
Patterns of Discrete Random Variables
443(8)
The Expected Time to a Maximal Run of Distinct Values
451(2)
Increasing Runs of Continuous Random Variables
453(2)
The Insurance Ruin Problem
455(20)
Exercises
460(12)
References
472(3)
Queueing Theory
475(72)
Introduction
475(1)
Preliminaries
476(4)
Cost Equations
477(1)
Steady-State Probabilities
478(2)
Exponential Models
480(16)
A Single-Server Exponential Queueing System
480(7)
A Single-Server Exponential Queueing System Having Finite Capacity
487(3)
A Shoeshine Shop
490(3)
A Queueing System with Bulk Service
493(3)
Network of Queues
496(11)
Open Systems
496(5)
Closed Systems
501(6)
The System M / G / 1
507(3)
Preliminaries: Work and Another Cost Identity
507(1)
Application of Work to M / G / 1
508(1)
Busy Periods
509(1)
Variations on the M/G/1
510(9)
The M/G/1 with Random-Sized Batch Arrivals
510(2)
Priority Queues
512(3)
An M/G/1 Optimization Example
515(4)
The Model G/M/1
519(6)
The G/M/1 Busy and Idle Periods
524(1)
A Finite Source Model
525(3)
Multiserver Queues
528(19)
Erlang's Loss System
529(1)
The M/M/k Queue
530(1)
The G/M/k Queue
530(2)
The M/G/k Queue
532(2)
Exercises
534(12)
References
546(1)
Reliability Theory
547(54)
Introduction
547(1)
Structure Functions
547(7)
Minimal Path and Minimal Cut Sets
550(4)
Reliability of Systems of Independent Components
554(5)
Bounds on the Reliability Function
559(12)
Method of Inclusion and Exclusion
560(9)
Second Method for Obtaining Bounds on r(p)
569(2)
System Life as a Function of Component Lives
571(9)
Expected System Lifetime
580(6)
An Upper Bound on the Expected Life of a Parallel System
584(2)
Systems with Repair
586(15)
A Series Model with Suspended Animation
591(2)
Exercises
593(7)
References
600(1)
Brownian Motion and Stationary Processes
601(38)
Brownian Motion
601(4)
Hitting Times, Maximum Variable, and the Gambler's Ruin Problem
605(2)
Variations on Brownian Motion
607(1)
Brownian Motion with Drift
607(1)
Geometric Brownian Motion
607(1)
Pricing Stock Options
608(12)
An Example in Options Pricing
608(3)
The Arbitrage Theorem
611(3)
The Black-Scholes Option Pricing Formula
614(6)
White Noise
620(2)
Gaussian Processes
622(3)
Stationary and Weakly Stationary Processes
625(5)
Harmonic Analysis of Weakly Stationary Processes
630(9)
Exercises
633(5)
References
638(1)
Simulation
639(70)
Introduction
639(5)
General Techniques for Simulating Continuous Random Variables
644(9)
The Inverse Transformation Method
644(1)
The Rejection Method
645(4)
The Hazard Rate Method
649(4)
Special Techniques for Simulating Continuous Random Variables
653(8)
The Normal Distribution
653(3)
The Gamma Distribution
656(1)
The Chi-Squared Distribution
657(1)
The Beta (n, m) Distribution
657(1)
The Exponential Distribution---The Von Neumann Algorithm
658(3)
Simulating from Discrete Distributions
661(7)
The Alias Method
664(4)
Stochastic Processes
668(11)
Simulating a Nonhomogeneous Poisson Process
669(7)
Simulating a Two-Dimensional Poisson Process
676(3)
Variance Reduction Techniques
679(17)
Use of Antithetic Variables
680(4)
Variance Reduction by Conditioning
684(4)
Control Variates
688(2)
Importance Sampling
690(6)
Determining the Number of Runs
696(1)
Coupling from the Past
696(13)
Exercises
699(8)
References
707(2)
Appendix: Solutions to Starred Exercises 709(40)
Index 749

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.