Author | Haight, Frank A. author |
---|---|
Title | Applied Probability [electronic resource] / by Frank A. Haight |
Imprint | Boston, MA : Springer US : Imprint: Springer, 1981 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-6467-6 |
Descript | XI, 290 p. online resource |
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 Bayesโ 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 DistributionsโThe 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 Gamblerโs 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: Borelโs 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