Introduction to Probability Models
Námskeið
- STÆ203G Líkindareikningur og tölfræði
- T-640 Financial Computer Tech.
- T-811-PROB Hagnýt líkindafræði
Ensk lýsing:
Introduction to Probability and Statistics for Engineers and Scientists provides a superior introduction to applied probability and statistics for engineering or science majors. Ross emphasizes the manner in which probability yields insight into statistical problems; ultimately resulting in an intuitive understanding of the statistical procedures most often used by practicing engineers and scientists.
Real data sets are incorporated in a wide variety of exercises and examples throughout the book, and this emphasis on data motivates the probability coverage. As with the previous editions, Ross' text has tremendously clear exposition, plus real-data examples and exercises throughout the text. Numerous exercises, examples, and applications connect probability theory to everyday statistical problems and situations.
Clear exposition by a renowned expert author Real data examples that use significant real data from actual studies across life science, engineering, computing and business End of Chapter review material that emphasizes key ideas as well as the risks associated with practical application of the material 25% New Updated problem sets and applications, that demonstrate updated applications to engineering as well as biological, physical and computer science New additions to proofs in the estimation section New coverage of Pareto and lognormal distributions, prediction intervals, use of dummy variables in multiple regression models, and testing equality of multiple population distributions.
Lýsing:
Introduction to Probability Models, Twelfth Edition , is the latest version of Sheldon Ross's classic bestseller. This trusted book introduces the reader to elementary probability modelling 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 research. The hallmark features of this text have been retained in this edition, including a superior writing style and excellent exercises and examples covering the wide breadth of coverage of probability topics.
In addition, many real-world applications in engineering, science, business and economics are included. Winner of a 2020 Textbook Excellence Award (College) ( Texty ) from the Textbook and Academic Authors Association Retains the valuable organization and trusted coverage that students and professors have relied on since 1972 Includes new coverage on coupling methods, renewal theory, queueing theory, and a new derivation of Poisson process Offers updated examples and exercises throughout, along with required material for Exam 3 of the Society of Actuaries.
Annað
- Höfundur: Sheldon M. Ross
- Útgáfa:12
- Útgáfudagur: 2019-03-09
- Engar takmarkanir á útprentun
- Engar takmarkanir afritun
- Format:Page Fidelity
- ISBN 13: 9780128143476
- Print ISBN: 9780128143469
- ISBN 10: 0128143479
Efnisyfirlit
- Introduction to Probability Models
- Copyright
- Contents
- Preface
- New to This Edition
- Course
- Examples and Exercises
- Organization
- Acknowledgments
- 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
- 1.7 Probability Is a Continuous Event Function
- Exercises
- References
- 2 Random Variables
- 2.1 Random Variables
- 2.2 Discrete Random Variables
- 2.2.1 The Bernoulli Random Variable
- 2.2.2 The Binomial Random Variable
- 2.2.3 The Geometric Random Variable
- 2.2.4 The Poisson Random Variable
- 2.3 Continuous Random Variables
- 2.3.1 The Uniform Random Variable
- 2.3.2 Exponential Random Variables
- 2.3.3 Gamma Random Variables
- 2.3.4 Normal Random Variables
- 2.4 Expectation of a Random Variable
- 2.4.1 The Discrete Case
- 2.4.2 The Continuous Case
- 2.4.3 Expectation of a Function of a Random Variable
- 2.5 Jointly Distributed Random Variables
- 2.5.1 Joint Distribution Functions
- 2.5.2 Independent Random Variables
- 2.5.3 Covariance and Variance of Sums of Random Variables
- Properties of Covariance
- 2.5.4 Joint Probability Distribution of Functions of Random Variables
- 2.6 Moment Generating Functions
- 2.6.1 The Joint Distribution of the Sample Mean and Sample Variance from a Normal Population
- 2.7 Limit Theorems
- 2.8 Proof of the Strong Law of Large Numbers
- 2.9 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
- 3.4.1 Computing Variances by Conditioning
- 3.5 Computing Probabilities by Conditioning
- 3.6 Some Applications
- 3.6.1 A List Model
- 3.6.2 A Random Graph
- 3.6.3 Uniform Priors, Polya's Urn Model, and Bose-Einstein Statistics
- 3.6.4 Mean Time for Patterns
- 3.6.5 The k-Record Values of Discrete Random Variables
- 3.6.6 Left Skip Free Random Walks
- 3.7 An Identity for Compound Random Variables
- 3.7.1 Poisson Compounding Distribution
- 3.7.2 Binomial Compounding Distribution
- 3.7.3 A Compounding Distribution Related to the Negative Binomial
- Exercises
- 4 Markov Chains
- 4.1 Introduction
- 4.2 Chapman-Kolmogorov Equations
- 4.3 Classification of States
- 4.4 Long-Run Proportions and Limiting Probabilities
- 4.4.1 Limiting Probabilities
- 4.5 Some Applications
- 4.5.1 The Gambler's Ruin Problem
- 4.5.2 A Model for Algorithmic Efficiency
- 4.5.3 Using a Random Walk to Analyze a Probabilistic Algorithm for the Satisfiability Problem
- 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
- 4.11.1 Predicting the States
- Exercises
- References
- 5 The Exponential Distribution and the Poisson Process
- 5.1 Introduction
- 5.2 The Exponential Distribution
- 5.2.1 Definition
- 5.2.2 Properties of the Exponential Distribution
- 5.2.3 Further Properties of the Exponential Distribution
- 5.2.4 Convolutions of Exponential Random Variables
- 5.2.5 The Dirichlet Distribution
- 5.3 The Poisson Process
- 5.3.1 Counting Processes
- 5.3.2 Definition of the Poisson Process
- 5.3.3 Further Properties of Poisson Processes
- 5.3.4 Conditional Distribution of the Arrival Times
- 5.3.5 Estimating Software Reliability
- 5.4 Generalizations of the Poisson Process
- 5.4.1 Nonhomogeneous Poisson Process
- 5.4.2 Compound Poisson Process
- Examples of Compound Poisson Processes
- 5.4.3 Conditional or Mixed Poisson Processes
- 5.5 Random Intensity Functions and Hawkes Processes
- 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 Pij(t)
- 6.5 Limiting Probabilities
- 6.6 Time Reversibility
- 6.7 The Reversed Chain
- 6.8 Uniformization
- 6.9 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
- 7.5.1 Alternating Renewal Processes
- 7.6 Semi-Markov Processes
- 7.7 The Inspection Paradox
- 7.8 Computing the Renewal Function
- 7.9 Applications to Patterns
- 7.9.1 Patterns of Discrete Random Variables
- 7.9.2 The Expected Time to a Maximal Run of Distinct Values
- 7.9.3 Increasing Runs of Continuous Random Variables
- 7.10 The Insurance Ruin Problem
- Exercises
- References
- 8 Queueing Theory
- 8.1 Introduction
- 8.2 Preliminaries
- 8.2.1 Cost Equations
- 8.2.2 Steady-State Probabilities
- 8.3 Exponential Models
- 8.3.1 A Single-Server Exponential Queueing System
- 8.3.2 A Single-Server Exponential Queueing System Having Finite Capacity
- 8.3.3 Birth and Death Queueing Models
- 8.3.4 A Shoe Shine Shop
- 8.3.5 Queueing Systems with Bulk Service
- 8.4 Network of Queues
- 8.4.1 Open Systems
- 8.4.2 Closed Systems
- 8.5 The System M/G/1
- 8.5.1 Preliminaries: Work and Another Cost Identity
- 8.5.2 Application of Work to M/G/1
- 8.5.3 Busy Periods
- 8.6 Variations on the M/G/1
- 8.6.1 The M/G/1 with Random-Sized Batch Arrivals
- 8.6.2 Priority Queues
- 8.6.3 An M/G/1 Optimization Example
- 8.6.4 The M/G/1 Queue with Server Breakdown
- 8.7 The Model G/M/1
- 8.7.1 The G/M/1 Busy and Idle Periods
- 8.8 A Finite Source Model
- 8.9 Multiserver Queues
- 8.9.1 Erlang's Loss System
- 8.9.2 The M/M/k Queue
- 8.9.3 The G/M/k Queue
- 8.9.4 The M/G/k Queue
- Exercises
- 9 Reliability Theory
- 9.1 Introduction
- 9.2 Structure Functions
- 9.2.1 Minimal Path and Minimal Cut Sets
- 9.3 Reliability of Systems of Independent Components
- 9.4 Bounds on the Reliability Function
- 9.4.1 Method of Inclusion and Exclusion
- 9.4.2 Second Method for Obtaining Bounds on r(p)
- 9.5 System Life as a Function of Component Lives
- 9.6 Expected System Lifetime
- 9.6.1 An Upper Bound on the Expected Life of a Parallel System
- 9.7 Systems with Repair
- 9.7.1 A Series Model with Suspended Animation
- 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
- 10.3.1 Brownian Motion with Drift
- 10.3.2 Geometric Brownian Motion
- 10.4 Pricing Stock Options
- 10.4.1 An Example in Options Pricing
- 10.4.2 The Arbitrage Theorem
- 10.4.3 The Black-Scholes Option Pricing Formula
- 10.5 The Maximum of Brownian Motion with Drift
- 10.6 White Noise
- 10.7 Gaussian Processes
- 10.8 Stationary and Weakly Stationary Processes
- 10.9 Harmonic Analysis of Weakly Stationary Processes
- Exercises
- References
- 11 Simulation
- 11.1 Introduction
- 11.2 General Techniques for Simulating Continuous Random Variables
- 11.2.1 The Inverse Transformation Method
- 11.2.2 The Rejection Method
- 11.2.3 The Hazard Rate Method
- Hazard Rate Method for Generating S: λs(t)=λ (t)
- 11.3 Special Techniques for Simulating Continuous Random Variables
- 11.3.1 The Normal Distribution
- 11.3.2 The Gamma Distribution
- 11.3.3 The Chi-Squared Distribution
- 11.3.4 The Beta (n, m) Distribution
- 11.3.5 The Exponential Distribution-The Von Neumann Algorithm
- 11.4 Simulating from Discrete Distributions
- 11.4.1 The Alias Method
- 11.5 Stochastic Processes
- 11.5.1 Simulating a Nonhomogeneous Poisson Process
- Method 1. Sampling a Poisson Process
- Method 2. Conditional Distribution of the Arrival Times
- Method 3. Simulating the Event Times
- 11.5.2 Simulating a Two-Dimensional Poisson Process
- 11.5.1 Simulating a Nonhomogeneous Poisson Process
- 11.6 Variance Reduction Techniques
- 11.6.1 Use of Antithetic Variables
- 11.6.2 Variance Reduction by Conditioning
- 11.6.3 Control Variates
- 11.6.4 Importance Sampling
- 11.7 Determining the Number of Runs
- 11.8 Generating from the Stationary Distribution of a Markov Chain
- 11.8.1 Coupling from the Past
- 11.8.2 Another Approach
- Exercises
- References
- 12.1 A Brief Introduction
- 12.2 Coupling and Stochastic Order Relations
- 12.3 Stochastic Ordering of Stochastic Processes
- 12.4 Maximum Couplings, Total Variation Distance, and the Coupling Identity
- 12.5 Applications of the Coupling Identity
- 12.5.1 Applications to Markov Chains
- 12.6 Coupling and Stochastic Optimization
- 12.7 Chen-Stein Poisson Approximation Bounds
- Exercises
- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- Chapter 6
- Chapter 7
- Chapter 8
- Chapter 9
- Chapter 10
- Chapter 11
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- Gerð : 208
- Höfundur : Ross, Sheldon M. , Sheldon M. Ross
- Útgáfuár : 2014
- Leyfi : 379