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Probability models: with business applications

Author: Shook, Robert C. ; Highland, Harold Joseph ; Highland, Esther H. Series: Irwin series in quantitative analysis for business Publisher: Irwin, 1969.Language: EnglishDescription: 592 p. : Graphs ; 24 cm.Type of document: BookBibliography/Index: Includes bibliographical references and index
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Book Europe Campus
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Print QA303 .S46 1969
(Browse shelf)
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Includes bibliographical references and index


Probability Models With Business Applications Table of Contents List of figures Part I. A probability model is developed from intuition about odds 1. When action must be taken now 1-1. The do or don't case. 1-2. Odds and probabilities. 1-3. A simple probability model. 1-4. Numerically valued sample spaces. 1-5. Expected value of an act. 1-6. Procedure for finding expected value of an act. 1-7. Expected value versus expected utility. 1-8. A multiple-choice problemCompetitive bidding. 1-9. Tree diagrams. 1-10. Probability trees. 1-11. Decis ion trees. 1-12. A multistage problem-Single-stage procedure. 1-13. A Multistage problem-Multistage procedure. 1-14. Comparison of solution methods-Multistage problems. xv 1 4 2. Elementary probability models 2-1. Experiments and events. 2-2. Special events; Relations between two events. 2-3. Venn diagrams. 2-4. Describing events. 2-5. The probability assignment. 2-6. Conditional probability. 2-7. Conditioning the sample space. 2-8. Independent events. 2-9. Bayes' Theorem. 2-10. Counting formulas. 2-11. Using the counting formulas. 2-12. Independent trials. 2-13. Bernoulli trials; Binomial probabilities. 56 3. When more information can be obtained: Decision problems involving compound experiments 3-1. How much''to spend? 3-2. An artificial problem. 3-3. Expected cost of uncertainty; Maximum sample size. 3-4. E(n = 2). 3-5. Choice of optimal sample size. 3-6. The sample space; The problem of dimensionality. 3-7. The (n,c) decision rule. 3-8. E((n,c)). 3-9. Generating an optimal sequence. 3-10. Finding (n*, c*). 3-11. Other methods of finding (n*, c*). 3-12. Computer program; Inventory decision making. 107 4. Simulation models 4-1. Applications of simulation models. 4-2. An inventory problem. 4-3. Outcome generators. 4-4. Verbal simulation model. 4-5. Simulation work form. 4-6. Inventory simulation procedure chart. 135 4-7. Planning the simulation runs. 4-8. Variable lead time simulator. 4-9. Two-variable inventory simulation procedure chart. 4-10. Comments about inventory simulation. 4-11. Tool crib simulation. 4-12. Tool crib problem parameters. 4-13. Arrival and service time generators. 4-14. Tool crib simulation work form. 4-15. Computer simulation model; Flow chart and procedure. 4-16. Evaluation of tool crib, simulations. 4-17. Computer programs: Inventory simulation models. 4-18. Computer program: Queue simulation model. Part II. Random variable models 5. The random variable model 5-1. Functions and random variables. 5-2. Probability distribution of a random variable. 5-3. The random variable model. 5-4. Joint probability distributions. 5-5. Independent random variables. 5-6. Expectations of a random variable. 5-7. Covariance. 5-8. Sums of random variables. 5-9. Mean and variance; Binomial distribution. 5-10. Conditional expectation. 233 236 6. The random event model: Discrete time 6-1. Bernoulli process; A model for random events in discrete time. 6-2. Waiting times; Geometric distributions. 6-3. Mean and variance; Geometric distribution. 6-4. The Pascal distribution. 6-5. Random event models; Summary. 266 7. The random event model: Continuous time 7-1. Poisson process; A model for random events in continuous time. 7-2. Some properties of the Poisson distribution. 7-3. The exponential density function. 7-4. The exponential distribution function. 7-5. The gamma density and distribution functions. 7-6. Comparison of Bernoulli and Poisson processes. 7-7. A steady-state queuing model. 7-8. Random arrival generator. 7-9. Computer program; Basic queue generator. 282 8. Random sampling models 8-1. Classification according to manager's interest. 8-2. The mean value sampling model. 8-3. Use of the sampling model in the interpretation of sample information. 8-4. Interval estimates of u, , known. 8-5. Testing beliefs about, u, , known. 8-6. Determination of sample size. 8-7. Mean value sampling model for finite population. 8-8. Inferences about u, , when Q is unknown. 8-9. The p-sampling model. 8-10. Variance testing sampling models. 8-11. The distribution testing sampling model. 8-12. Some additional formulas. 320 Part III. Random process models 9. Description of a random process 9-1. Sample space of a Bernoulli process. 9-2. Significance of the state space. 9-3. Four classes of random processes illustrated. 9-4. Computer program; Markov chains. 371 377 10. Generating functions 10-1. Need for new techniques. 10-2. Generating functions. 10-3. Convolutions. 10-4. Finding distributions by the method of generating functions. 10-5. Derived functions. 10-6. Finding expected values and variances by the method of generating functions. 10-7. An application of the method of generating functions. 398 11. Compound distributions and branching processes 11-1. A random number of random variables. 11-2. Two special compound distributions. 11-3. Compound Poisson distribution. 11-4. Expectation and variance of a compound distribution. 11-5. Branching processes. 11-6. Expected number of descendants in the nth generation. 11-7. Variance in realizations of a branching process. 11-8. Applications of branching processes. 418 12. The renewal process 12-1. The replacement problem. 12-2. Renewal process; One new part. 12-3. Renewal process; One part aged k. 12-4. Renewal process; Many parts with different ages. 441 Appendixes. Appendix A. How to read and design a procedure chart Appendix B. Recommended readings Appendix C. Tables Appendix D. Answers to problems Appendix E. Glossary of formulas 451 453 462 467 553 573 585 Index

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