Introduction to Probability Models
Sheldon M. Ross
- 出版商: Academic Press
- 出版日期: 2014-09-25
- 售價: $3,220
- 貴賓價: 9.5 折 $3,059
- 語言: 英文
- 頁數: 568
- 裝訂: Paperback
- ISBN: 1483245799
- ISBN-13: 9781483245799
-
相關分類:
機率統計學 Probability-and-statistics
海外代購書籍(需單獨結帳)
相關主題
商品描述
Introduction to Probability Models, Fifth Edition focuses on different probability models of natural phenomena.
This edition includes additional material in Chapters 5 and 10, such as examples relating to analyzing algorithms, minimizing highway encounters, collecting coupons, and tracking the AIDS virus. The arbitrage theorem and its relationship to the duality theorem of linear program are also covered, as well as how the arbitrage theorem leads to the Black-Scholes option pricing formula.
Other topics include the Bernoulli random variable, Chapman-Kolmogorov equations, and properties of the exponential distribution. The continuous-time Markov chains, single-server exponential queueing system, variations on Brownian motion; and variance reduction by conditioning are also elaborated.
This book is a good reference for students and researchers conducting work on probability models.
目錄大綱
Preface
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
2.2.1. 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. Joint Probability Distribution of Functions of 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
3.6.1. 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. In Normal Sampling X- and S2 are Independent
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
4.5.1. The Gambler's Ruin Problem
4.5.2. A Model for Algorithmic Efficiency
4.6. Branching Processes
4.7. Time Reversible Markov Chains
4.8. Markov Decision Processes
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
5.3. The Poisson Process
5.3.1. Counting Processes
5.3.2. Definition of the Poisson Process
5.3.3. Interarrival and Waiting Time Distributions
5.3.4. Further Properties of Poisson Processes
5.3.5. Conditional Distribution of the Arrival Times
5.3.6. Estimating Software Reliability
5.4. Generalizations of the Poisson Process
5.4.1. Nonhomogeneous Poisson Process
5.4.2. Compound 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 Kolmogorov Differential Equations
6.5. Limiting Probabilities
6.6. Time Reversibility
6.7. Uniformization
6.8. Computing the Transition Probabilities
ExercisesReferences
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
9.7. 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
10.3.1. 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. 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
11.2.1. The Inverse Transformation Method 498
11.2.2. The Rejection Method
11.2.3. Hazard Rate Method
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
11.5.2. Simulating a Two-Dimensional 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
11.7. Determining the Number of Runs
Exercises
References
Index
