Introduction to probability models:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Acad. Press
2003
|
| Ausgabe: | 8. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 755 S. |
| ISBN: | 0125980558 |
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Datensatz im Suchindex
| _version_ | 1804129894946308096 |
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| adam_text | INTRODUCTION TO PROBABILITY MODELS EIGHTH EDITION SHELDON M. ROSS
UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA ACADEMIC PRESS AN IMPRINT
OFELSEVIER AMSTERDAM BOSTON LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN
FRANCISCO SINGAPORE SYDNEY TOKYO CONTENTS PREFACE XIII 1. INTRODUCTION
TO PROBABILITY THEORY 1 1.1. INTRODUCTION 1 1.2. SAMPLE SPACE AND EVENTS
1 1.3. PROBABILITIES DEFINED ON EVENTS 4 1.4. CONDITIONAL PROBABILITIES
7 1.5. INDEPENDENT EVENTS 10 1.6. BAYES FORMULA 12 EXERCISES 15
REFERENCES 21 2. RANDOM VARIABLES 23 2.1. RANDOM VARIABLES 23 2.2.
DISCRETE RANDOM VARIABLES 27 2.2.1. THE BERNOULLI RANDOM VARIABLE 28
2.2.2. THE BINOMIAL RANDOM VARIABLE 29 2.2.3. THE GEOMETRIC RANDOM
VARIABLE 31 2.2.4. THE POISSON RANDOM VARIABLE 32 2.3. CONTINUOUS RANDOM
VARIABLES 34 2.3.1. THE UNIFORM RANDOM VARIABLE 35 2.3.2. EXPONENTIAL
RANDOM VARIABLES 36 2.3.3. GAMMA RANDOM VARIABLES 37 2.3.4. NORMAL
RANDOM VARIABLES 37 VI CONTENTS 2.4. EXPECTATION OF A RANDOM VARIABLE 38
2.4.1. THE DISCRETE CASE 38 2.4.2. THE CONTINUOUS CASE 41 2.4.3.
EXPECTATION OF A FUNCTION OF A RANDOM VARIABLE 43 2.5. JOINTLY
DISTRIBUTED RANDOM VARIABLES 47 2.5.1. JOINT DISTRIBUTION FUNCTIONS 47
2.5.2. INDEPENDENT RANDOM VARIABLES 51 2.5.3. COVARIANCE AND VARIANCE OF
SUMS OF RANDOM VARIABLES 53 2.5.4. JOINT PROBABILITY DISTRIBUTION OF
FUNCTIONS OF RANDOM VARIABLES 61 2.6. MOMENT GENERATING FUNCTIONS 64
2.6.1. THE JOINT DISTRIBUTION OF THE SAMPLE MEAN AND SAMPLE VARIANCE
FROM A NORMAL POPULATION 74 2.7. LIMIT THEOREMS 77 2.8. STOCHASTIC
PROCESSES 83 EXERCISES 85 REFERENCES 96 3. CONDITIONAL PROBABILITY AND
CONDITIONAL EXPECTATION 97 3.1. INTRODUCTION 97 3.2. THE DISCRETE CASE
97 3.3. THE CONTINUOUS CASE 102 3.4. COMPUTING EXPECTATIONS BY
CONDITIONING 105 3.4.1. COMPUTING VARIANCES BY CONDITIONING 116 3.5.
COMPUTING PROBABILITIES BY CONDITIONING 119 3.6. SOME APPLICATIONS 136
3.6.1. A LIST MODEL 136 3.6.2. A RANDOM GRAPH 138 3.6.3. UNIFORM PRIORS,
POLYA S URN MODEL, AND BOSE-EINSTEIN STATISTICS 146 3.6.4. MEAN TIME FOR
PATTERNS 150 3.6.5. A COMPOUND POISSON IDENTITY 154 3.6.6. THE /C-RECORD
VALUES OF DISCRETE RANDOM VARIABLES 158 EXERCISES 161 4. MARKOV CHAINS
181 4.1. INTRODUCTION 181 4.2. CHAPMAN-KOLMOGOROV EQUATIONS 185 4.3.
CLASSIFICATION OF STATES 189 CONTENTS VII 4.4. LIMITING PROBABILITIES
200 4.5. SOME APPLICATIONS 213 4.5.1. THE GAMBLER S RUIN PROBLEM 213
4.5.2. A MODEL FOR ALGORITHMIC EFFICIENCY 217 4.5.3. USING A RANDOM WALK
TO ANALYZE A PROBABILISTIC ALGORITHM FOR THE SATISFIABILITY PROBLEM 220
4.6. MEAN TIME SPENT IN TRANSIENT STATES 226 4.7. BRANCHING PROCESSES
228 4.8. TIME REVERSIBLE MARKOV CHAINS 232 4.9. MARKOV CHAIN MONTE CARLO
METHODS 243 4.10. MARKOV DECISION PROCESSES 248 EXERCISES 252 REFERENCES
268 5. THE EXPONENTIAL DISTRIBUTION AND THE POISSON PROCESS 269 5.1.
INTRODUCTION 269 5.2. THE EXPONENTIAL DISTRIBUTION 270 5.2.1. DEFINITION
270 5.2.2. PROPERTIES OF THE EXPONENTIAL DISTRIBUTION 272 5.2.3. FURTHER
PROPERTIES OF THE EXPONENTIAL DISTRIBUTION 279 5.2.4. CONVOLUTIONS OF
EXPONENTIAL RANDOM VARIABLES 284 5.3. THE POISSON PROCESS 288 5.3.1.
COUNTING PROCESSES 288 5.3.2. DEFINITION OF THE POISSON PROCESS 289
5.3.3. INTERARRIVAL AND WAITING TIME DISTRIBUTIONS 293 5.3.4. FURTHER
PROPERTIES OF POISSON PROCESSES 295 5.3.5. CONDITIONAL DISTRIBUTION OF
THE ARRIVAL TIMES 301 5.3.6. ESTIMATING SOFTWARE RELIABILITY 313 5.4.
GENERALIZATIONS OF THE POISSON PROCESS 316 5.4.1. NONHOMOGENEOUS POISSON
PROCESS 316 5.4.2. COMPOUND POISSON PROCESS 321 5.4.3. CONDITIONAL OR
MIXED POISSON PROCESSES 327 EXERCISES 330 REFERENCES 348 6.
CONTINUOUS-TIME MARKOV CHAINS 349 6.1. INTRODUCTION 349 6.2.
CONTINUOUS-TIME MARKOV CHAINS 350 6.3. BIRTH AND DEATH PROCESSES 352 VIM
CONTENTS 6.4. THE TRANSITION PROBABILITY FUNCTION P TJ (T) 359 6.5.
LIMITING PROBABILITIES 368 6.6. TIME REVERSIBILITY 376 6.7.
UNIFORMIZATION 384 6.8. COMPUTING THE TRANSITION PROBABILITIES 388
EXERCISES 390 REFERENCES 399 7. RENEWAL THEORY AND ITS APPLICATIONS 401
7.1. INTRODUCTION 401 7.2. DISTRIBUTION OF N(T) 403 7.3. LIMIT THEOREMS
AND THEIR APPLICATIONS 407 7.4. RENEWAL REWARD PROCESSES 416 7.5.
REGENERATIVE PROCESSES 425 7.5.1. ALTERNATING RENEWAL PROCESSES 428 7.6.
SEMI-MARKOV PROCESSES 434 7.7. THE INSPECTION PARADOX 437 7.8. COMPUTING
THE RENEWAL FUNCTION 440 7.9. APPLICATIONS TO PATTERNS 443 7.9.1.
PATTERNS OF DISCRETE RANDOM VARIABLES 443 7.9.2. THE EXPECTED TIME TO A
MAXIMAL RUN OF DISTINCT VALUES 451 7.9.3. INCREASING RUNS OF CONTINUOUS
RANDOM VARIABLES 453 7.10. THE INSURANCE RUIN PROBLEM 455 EXERCISES 460
REFERENCES 472 8. QUEUEING THEORY 475 8.1. INTRODUCTION 475 8.2.
PRELIMINARIES 476 8.2.1. COST EQUATIONS 477 8.2.2. STEADY-STATE
PROBABILITIES 478 8.3. EXPONENTIAL MODELS 480 8.3.1. A SINGLE-SERVER
EXPONENTIAL QUEUEING SYSTEM 480 8.3.2. A SINGLE-SERVER EXPONENTIAL
QUEUEING SYSTEM HAVING FINITE CAPACITY 487 8.3.3. A SHOESHINE SHOP 490
8.3.4. A QUEUEING SYSTEM WITH BULK SERVICE 493 8.4. NETWORK OF QUEUES
496 8.4.1. OPEN SYSTEMS 496 8.4.2. CLOSED SYSTEMS 501 CONTENTS IX 8.5.
THE SYSTEM M/G/L 507 8.5.1. PRELIMINARIES: WORK AND ANOTHER COST
IDENTITY 507 8.5.2. APPLICATION OF WORK TO M/G/L 508 8.5.3. BUSY PERIODS
509 8.6. VARIATIONS ON THE M/G/L 510 8.6.1. THE M/G/L WITH RANDOM-SIZED
BATCH ARRIVALS 510 8.6.2. PRIORITY QUEUES 512 8.6.3. AN M/G/L
OPTIMIZATION EXAMPLE 515 8.7. THE MODEL G/M/L 519 8.7.1. THE G/M/L BUSY
AND IDLE PERIODS 524 8.8. A FINITE SOURCE MODEL 525 8.9. MULTISERVER
QUEUES 528 8.9.1. ERLANG S LOSS SYSTEM 529 8.9.2. THE M/M/K QUEUE 530
8.9.3. THE G/M/K QUEUE 530 8.9.4. THE M/G/K QUEUE 532 EXERCISES 534
REFERENCES 546 9. RELIABILITY THEORY 547 9.1. INTRODUCTION 547 9.2.
STRUCTURE FUNCTIONS 547 9.2.1. MINIMAL PATH AND MINIMAL CUT SETS 550
9.3. RELIABILITY OF SYSTEMS OF INDEPENDENT COMPONENTS 554 9.4. BOUNDS ON
THE RELIABILITY FUNCTION 559 9.4.1. METHOD OF INCLUSION AND EXCLUSION
560 9.4.2. SECOND METHOD FOR OBTAINING BOUNDS ON RIP) 569 9.5. SYSTEM
LIFE AS A FUNCTION OF COMPONENT LIVES 571 9.6. EXPECTED SYSTEM LIFETIME
580 9.6.1. AN UPPER BOUND ON THE EXPECTED LIFE OF A PARALLEL SYSTEM 584
9.7. SYSTEMS WITH REPAIR 586 9.7.1. A SERIES MODEL WITH SUSPENDED
ANIMATION 591 EXERCISES 593 REFERENCES 600 10. BROWNIAN MOTION AND
STATIONARY PROCESSES 601 10.1. BROWNIAN MOTION 601 10.2. HITTING TIMES,
MAXIMUM VARIABLE, AND THE GAMBLER S RUIN PROBLEM 605 X CONTENTS 10.3.
VARIATIONS ON BROWNIAN MOTION 607 10.3.1. BROWNIAN MOTION WITH DRIFT 607
10.3.2. GEOMETRIC BROWNIAN MOTION 607 10.4. PRICING STOCK OPTIONS 608
10.4.1. AN EXAMPLE IN OPTIONS PRICING 608 10.4.2. THE ARBITRAGE THEOREM
611 10.4.3. THE BLACK-SCHOLES OPTION PRICING FORMULA 614 10.5. WHITE
NOISE 620 10.6. GAUSSIAN PROCESSES 622 10.7. STATIONARY AND WEAKLY
STATIONARY PROCESSES 625 10.8. HARMONIC ANALYSIS OF WEAKLY STATIONARY
PROCESSES 630 EXERCISES 633 REFERENCES 638 11. SIMULATION 639 11.1.
INTRODUCTION 639 11.2. GENERAL TECHNIQUES FOR SIMULATING CONTINUOUS
RANDOM VARIABLES 644 11.2.1. THE INVERSE TRANSFORMATION METHOD 644
11.2.2. THE REJECTION METHOD 645 11.2.3. THE HAZARD RATE METHOD 649
11.3. SPECIAL TECHNIQUES FOR SIMULATING CONTINUOUS RANDOM VARIABLES 653
11.3.1. THE NORMAL DISTRIBUTION 653 11.3.2. THE GAMMA DISTRIBUTION 656
11.3.3. THE CHI-SQUARED DISTRIBUTION 657 11.3.4. THE BETA (N, M)
DISTRIBUTION 657 11.3.5. THE EXPONENTIAL DISTRIBUTION*THE VON NEUMANN
ALGORITHM 658 11.4. SIMULATING FROM DISCRETE DISTRIBUTIONS 661 11.4.1.
THE ALIAS METHOD 664 11.5. STOCHASTIC PROCESSES 668 11.5.1. SIMULATING A
NONHOMOGENEOUS POISSON PROCESS 669 11.5.2. SIMULATING A TWO-DIMENSIONAL
POISSON PROCESS 676 11.6. VARIANCE REDUCTION TECHNIQUES 679 11.6.1. USE
OF ANTITHETIC VARIABLES 680 11.6.2. VARIANCE REDUCTION BY CONDITIONING
684 11.6.3. CONTROL VARIATES 688 11.6.4. IMPORTANCE SAMPLING 690 11.7.
DETERMINING THE NUMBER OF RUNS 696 CONTENTS XI 11.8. COUPLING FROM THE
PAST 696 EXERCISES 699 REFERENCES 707 APPENDIX: SOLUTIONS TO STARRED
EXERCISES 709 INDEX 749
|
| any_adam_object | 1 |
| author | Ross, Sheldon M. 1943- |
| author_GND | (DE-588)123762235 |
| author_facet | Ross, Sheldon M. 1943- |
| author_role | aut |
| author_sort | Ross, Sheldon M. 1943- |
| author_variant | s m r sm smr |
| building | Verbundindex |
| bvnumber | BV016976781 |
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| callnumber-label | QA273 |
| callnumber-raw | QA273 |
| callnumber-search | QA273 |
| callnumber-sort | QA 3273 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 170 |
| ctrlnum | (OCoLC)249116790 (DE-599)BVBBV016976781 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 8. ed. |
| format | Book |
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| id | DE-604.BV016976781 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:12:24Z |
| institution | BVB |
| isbn | 0125980558 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010252347 |
| oclc_num | 249116790 |
| open_access_boolean | |
| owner | DE-29T DE-898 DE-BY-UBR DE-634 DE-83 |
| owner_facet | DE-29T DE-898 DE-BY-UBR DE-634 DE-83 |
| physical | XVII, 755 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Acad. Press |
| record_format | marc |
| spelling | Ross, Sheldon M. 1943- Verfasser (DE-588)123762235 aut Introduction to probability models Sheldon M. Ross 8. ed. Amsterdam [u.a.] Acad. Press 2003 XVII, 755 S. txt rdacontent n rdamedia nc rdacarrier Stochastisches Modell - Stochastik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Modell (DE-588)4039798-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Stochastisches Modell (DE-588)4057633-4 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 1\p DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Modell (DE-588)4039798-1 s 2\p DE-604 Mathematisches Modell (DE-588)4114528-8 s 3\p DE-604 4\p DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010252347&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ross, Sheldon M. 1943- Introduction to probability models Stochastisches Modell - Stochastik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Modell (DE-588)4039798-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastisches Modell (DE-588)4057633-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4039798-1 (DE-588)4114528-8 (DE-588)4079013-7 (DE-588)4057633-4 (DE-588)4057630-9 |
| title | Introduction to probability models |
| title_auth | Introduction to probability models |
| title_exact_search | Introduction to probability models |
| title_full | Introduction to probability models Sheldon M. Ross |
| title_fullStr | Introduction to probability models Sheldon M. Ross |
| title_full_unstemmed | Introduction to probability models Sheldon M. Ross |
| title_short | Introduction to probability models |
| title_sort | introduction to probability models |
| topic | Stochastisches Modell - Stochastik Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Modell (DE-588)4039798-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastisches Modell (DE-588)4057633-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastisches Modell - Stochastik Wahrscheinlichkeitsrechnung Modell Mathematisches Modell Wahrscheinlichkeitstheorie Stochastisches Modell Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010252347&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rosssheldonm introductiontoprobabilitymodels |