Applied Probability

Applied Probability by Frank A. Haight.

Probability (including stochastic processes) is now being applied to virtually every academic discipline, especially to the sciences. An area of substantial application is that known as operations research or industrial engineering, which incorporates subjects such as queueing theory, optimization,...

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Bibliographic Details
Main Author: Haight, Frank A. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer US : Imprint: Springer, 1981.
Edition:1st ed. 1981.
Series:Mathematical Concepts and Methods in Science and Engineering ; 23
Springer eBook Collection.
Subjects:
Probabilities.
Operations research.
Decision making.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1. Discrete Probability
  • 1.1. Applied Probability
  • 1.2. Sample Spaces
  • 1.3. Probability Distributions and Parameters
  • 1.4. The Connection between Distributions and Sample Points: Random Variables
  • 1.5. Events and Indicators
  • 1.6. Mean and Variance
  • 1.7. Calculation of the Mean and Variance
  • 1.8. The Distribution Function
  • 1.9. The Gamma Function and the Beta Function
  • 1.10. The Negative Binomial Distribution
  • 1.11. The Probability Generating Function
  • 1.12. The Catalan Distribution
  • 1.13. More about the p.g.f.; The Equation s = ?(s)
  • 1.14. Problems
  • 2. Conditional Probability
  • 2.1. Introduction. An Example
  • 2.2. Conditional Probability and Bayes’ Theorem
  • 2.3. Conditioning
  • 2.4. Independence and Bernoulli Trials
  • 2.5. Moments, Distribution Functions, and Generating Functions
  • 2.6. Convolutions and Sums of Random Variables
  • 2.7. Computing Convolutions: Examples
  • 2.8. Diagonal Distributions
  • 2.9. Problems
  • 3. Markov Chains
  • 3.1. Introduction: Random Walk
  • 3.2. Definitions
  • 3.3. Matrix and Vector
  • 3.4. The Transition Matrix and Initial Vector
  • 3.5. The Higher-Order Transition Matrix: Regularity
  • 3.6. Reducible Chains
  • 3.7. Periodic Chains
  • 3.8. Classification of States. Ergodic Chains
  • 3.9. Finding Equilibrium Distributions—The Random Walk Revisited
  • 3.10. A Queueing Model
  • 3.11. The Ehrenfest Chain
  • 3.12. Branching Chains
  • 3.13. Probability of Extinction
  • 3.14. The Gambler’s Ruin
  • 3.15. Probability of Ruin as Probability of Extinction
  • 3.16. First-Passage Times
  • 3.17. Problems
  • 4. Continuous Probability Distributions
  • 4.1. Examples
  • 4.2. Probability Density Functions
  • 4.3. Change of Variables
  • 4.4. Convolutions of Density Functions
  • 4.5. The Incomplete Gamma Function
  • 4.6. The Beta Distribution and the Incomplete Beta Function
  • 4.7. Parameter Mixing
  • 4.8. Distribution Functions
  • 4.9. Stieltjes Integration
  • 4.10. The Laplace Transform
  • 4.11. Properties of the Laplace Transform
  • 4.12. Laplace Inversion
  • 4.13. Random Sums
  • 4.14. Problems
  • 5. Continuous Time Processes
  • 5.1. Introduction and Notation
  • 5.2. Renewal Processes
  • 5.3. The Poisson Process
  • 5.4. Two-State Processes
  • 5.5. Markov Processes
  • 5.6. Equilibrium
  • 5.7. The Method of Marks
  • 5.8. The Markov Infinitesimal Matrix
  • 5.9. The Renewal Function
  • 5.10. The Gap Surrounding an Arbitrary Point
  • 5.11. Counting Distributions
  • 5.12. The Erlang Process
  • 5.13. Displaced Gaps
  • 5.14. Divergent Birth Processes
  • 5.15. Problems
  • 6. The Theory of Queues
  • 6.1. Introduction and Classification
  • 6.2. The M? / M? / 1 Queue: General Solution
  • 6.3. The M? / M? / 1 Queue: Oversaturation
  • 6.4. The M? / M? / 1 Queue: Equilibrium
  • 6.5. The M? / M? / n Queue in Equilibrium: Loss Formula
  • 6.6. The M? / G? / 1 Queue and the Imbedded Markov Chain
  • 6.7. The Pollaczek-Khintchine Formula
  • 6.8. Waiting Time
  • 6.9. Virtual Queueing Time
  • 6.10. The Equation y = xe?x
  • 6.11. Busy Period: Borel’s Method
  • 6.12. The Busy Period Treated as a Branching Process: The M / G /1 Queue
  • 6.13. The Continuous Busy Period and the M / G /1 Queue
  • 6.14. Generalized Busy Periods
  • 6.15. The G / M /1 Queue
  • 616 Balking
  • 6.17. Priority Service
  • 6.18. Reverse-Order Service (LIFO)
  • 6.19. Problems.

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