Probability and random processes for electrical engineers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
WCB McGraw-Hill
1998
|
| Schriftenreihe: | McGraw-Hill series in electrical and computer engineering
Communications and signal processing |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 676 S. Ill., graph. Darst. |
| ISBN: | 0070674914 |
Internformat
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| 650 | 4 | |a Electrical engineering |x Mathematics | |
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Datensatz im Suchindex
| _version_ | 1804126345488236544 |
|---|---|
| adam_text | IMAGE 1
P R O B A B I L I TY AND
R A N D OM P R O C E S S ES FOR E L E C T R I C AL E N G I N E E RS
Y A N N IS VINIOTIS N O R TH C A R O L I NA S T A TE U N I V E R S I TY
WCB
MCGRAW-HILL
B O S T ON B U RR R I D G E, IL D U B U Q U E, IA M A D I S O N, WL NEW
YORK S AN FRANCISCO S T. L O U IS
BANGKOK BOGATAE CARACAS L I S B ON LONDON M A D R ID
M E X I CO CITY MILAN N EW D E L HI S E O UL S I N G A P O RE SYDNEY
TAIPEI TORONTO
IMAGE 2
C O N T E N TS
PREFACE XV
INTRODUCTION 1
1.1 WHY THIS COURSE? 2
1.2 WHY AN ABSTRACT THEORY? 6
1.3 WHY PROBABILITY THEORY? 7
1.4 WHAT CAN PROBABILITY THEORY DO? 7
1.5 WHAT IS THE THEORY IN A NUTSHELL? 7
1.6 MODELING TOOLS? 9
1.7 MAIN MODELS? 9
1.8 MAIN APPLICATION AREAS 10
1.9 A FEW DETAILED EXAMPLES 11
1.10 D I DL LEARN THE THEORY? 18
1.11 WHERE DO I LEARN MORE? 18
1.12 SUMMARY OF MAIN POINTS 19
1.13 PROBLEMS 20
B A S IC C O N C E P TS 23
2.1 RANDOM EXPERIMENTS 24
2.2 SAMPLE SPACES AND OUTCOMES 26
2.3 EVENTS 27
2.4 PROBABILITY AXIOMS AND THE SETS OF INTEREST 30
2.5 ELEMENTARY THEOREMS 33
2.6 CONDITIONAL PROBABILITIES 35
2.7 INDEPENDENT EVENTS 40
2.8 HOW DO WE ASSIGN PROBABILITIES TO EVENTS? 42
2.9 PROBABILISTIC MODELING 44
2.10 DIFFICULTIES 46
2.11 SUMMARY OF MAIN POINTS 46
IX
IMAGE 3
2.12 CHECKHST OF IMPORTANT TOOLS
2.13 PROBLEMS
47 47
C O N C E PT OF A R A N D OM VARIABLE 67
3.1 SETS OFTHE FORM (-OO.AR] 68
3.2 CONCEPT OF A RANDOM VARIABLE 70
3.3 CUMULATIVE DISTRIBUTION FUNCTION 76
3.4 PROBABILITY DENSITY FUNCTION 82
3.5 PROBABILISTIC MODEL REVISITED 95
3.6 USEFUL RAN DORN VARIABLE MODELS 95
3.7 HISTOGRAMS 109
3.8 TRANSFORMATIONS OF A RANDOM VARIABLE 115
3.9 MOMENTS OF RANDOM VARIABLES 121
3.10 RELIABILITY AND FAILURE RATES 129
3.11 TRANSFORMS OF PROBABILITY DENSITY FUNCTIONS 134
3.12 TAIL INEQUALITIES 139
3.13 GENERATION OF VALUES OF A RANDOM VARIABLE 145
3.14 SUMMARY OF MAIN POINTS 150
3.15 CHECKLIST OF IMPORTANT TOOLS 151
3.16 PROBLEMS 152
A V E C T OR R A N D OM VARIABLE 195
4.1 EXPERIMENTS WITH MORE THAN ONE MEASUREMENT 196
4.2 THE SETS (-OO, X] X (-OO, Y] 198
4.3 JOINT CUMULATIVE DISTRIBUTION FUNCTION 204
4.4 JOINT PROBABILITY DENSITY FUNCTION 212
4.5 PROBABILISTIC MODEL REVISITED 221
4.6 CONDITIONAL PROBABILITIES AND DENSITIES 223
4.7 INDEPENDENCE 230
4.8 TRANSFORMATIONS OF A RANDOM VECTOR 236
4.9 EXPECTATION, COVARIANCE, AND CORRELATION COEFFICIENT 256
4.10 USEFUL JOINT DISTRIBUTIONS 260
4.11 MORE THAN TWO RANDOM VARIABLES 264
4.12 GENERATION OF VALUES OF A RANDOM VECTOR 270
4.13 SUMMARY OF MAIN POINTS 272
4.14 CHECKLIST OF IMPORTANT TOOLS 273
4.15 PROBLEMS 273
IMAGE 4
CONTENTS XI
5 I N T R O D U C T I ON TO E S T I M A T I ON 303
5.1 CRITERIA TO CONSIDER 304
5.2 MMSE ESTIMATION, SINGLE MEASUREMENT 307
5.3 LINEAR PREDICTION, MULTIPLE MEASUREMENTS 315
5.4 DOW JONES EXAMPLE 318
5.5 MAXIMUM-LIKELIHOOD ESTIMATION 322
5.6 AN HISTORICAL REMARK 324
5.7 SUMMARY OF MAIN POINTS 327
5.8 CHECKLIST OF IMPORTANT TOOLS 327
5.9 PROBLEMS 327
6 S E Q U E N C ES OF (HD) R A N D OM VARIABLES 333
6.1 EXPERIMENTS WITH AN UNBOUNDED NUMBER OF MEASUREMENTS 333 6.2 HD
RANDOM VARIABLES 334
6.3 SUMS OF HD RANDOM VARIABLES 335
6.4 RANDOM SUMS OF HD RANDOM VARIABLES 340
6.5 WEAK LAW OF LARGE NUMBERS 344
6.6 STRONG LAW OF LARGE NUMBERS 347
6.7 CENTRAL LIMIT THEOREM 350
6.8 CONVERGENCE OF SEQUENCES OF RANDOM VARIABLES 355
6.9 BOREL-CANTELLI LEMMAS 366
6.10 SUMMARY OF MAIN POINTS 368
6.11 CHECKLIST OF IMPORTANT TOOLS 369
6.12 PROBLEMS 369
7 R A N D OM P R O C E S S ES 387
7.1 DEFINITION OF A RANDOM PROCESS AND EXAMPLES 388
7.2 JOINT CDF AND PDF 393
7.3 EXPECTATION, AUTOCOVARIANCE, AND CORRELATION FUNCTIONS 398
7.4 SOME IMPORTANT SPECIAL CASES 399
7.5 USEFUL RANDOM PROCESS MODELS 406
7.6 CONTINUITY, DERIVATIVES, AND INTEGRALS 409
7.7 ERGODICITY 413
7.8 KARHUNEN-LOEVE EXPANSIONS 417
7.9 GENERATION OF VALUES OF A RANDOM PROCESS 420
IMAGE 5
CONTENTS
7.10 SUMMARY OF MAIN POINTS 421
7.11 CHECKLIST OF IMPORTANT TOOLS 422
7.12 PROBLEMS 422
P O I S S ON A ND GAUSSIAN R A N D OM P R O C E S S ES 439
8.1 POISSON PROCESS 439
8.2 GAUSSIAN RANDOM PROCESS 458
8.3 SUMMARY OF MAIN POINTS 463
8.4 CHECKLIST OF IMPORTANT TOOLS 464
8.5 PROBLEMS 464
P R O C E S S I NG OF R A N D OM P R O C E S S ES 475
9.1 INTRODUCTION 475
9.2 POWER SPECTRAL DENSITY FUNCTION 477
9.3 RESPONSE OF LINEAR SYSTEMS TO RAN DORN PROCESSES 484
9.4 OPTIMAL LINEAR ESTIMATION 492
9.5 KAIMAN FILTER 503
9.6 PERIODOGRAMS 510
9.7 SUMMARY OF MAIN POINTS 513
9.8 CHECKLIST OF IMPORTANT TOOLS 513
9.9 PROBLEMS 514
M A R K OV C H A I NS 527
10.1 DEFINITION AND CLASSIFICATION 528
10.2 DISCRETE-TIME MARKOV CHAINS 535
10.3 STEADY STATE OF MARKOV CHAINS 541
10.4 DRIFTS AND ERGODICITY 557
10.5 CONTINUOUS-TIME MARKOV CHAINS 561
10.6 APPLICATION TO ETHERNET LANS 571
10.7 GENERATION OF VALUES OF A MARKOV CHAIN 574
10.8 SUMMARY OF MAIN POINTS 576
10.9 CHECKLIST OF IMPORTANT TOOLS 576
10.10 PROBLEMS 576
IMAGE 6
CONTENTS XIII
11 CASE STUDY: A BUS-BASED S W I T CH A R C H I T E C T U RE 595
11.1 SWITCH ARCHITECTURE AND OPERATION 596
11.2 TRANSITION TO A STOCHASTIC MODEL 598
11.3 SYSTEM MODEL 599
11.4 PERFORMANCE MEASURES 601
11.5 INPUT DATA DESCRIPTION 603
11.6 DISCUSSION OF RESULTS 604
11.7 DESCRIPTION OF THE SIMULATOR 610
A S ET T H E O RY P R I M ER 611
A.L SETS AND SUBSETS 611
A.2 OPERATIONS ON SETS 618
A.3 PARTITIONS OF A SET 624
A.4 LIMITS OF SEQUENCES OF SETS 624
A.5 ALGEBRAS OF SETS 625
A.6 PROBLEMS 626
B C O U N T I NG M E T H O DS 633
B.L ORDERING OF ELEMENTS 633
B.2 SAMPLING WITH ORDERING AND WITHOUT REPLACEMENT OF ELE MENTS 634
B.3 SAMPLING WITHOUT ORDERING AND WITHOUT REPLACEMENT OF ELEMENTS 635
B.4 SAMPLING WITHOUT ORDERING AND WITH REPLACEMENT OF ELE MENTS 637
B.5 PROBLEMS 638
C H I S T O R I C AL D E V E L O P M E NT OF T HE T H E O RY 643
C.L A BRIEF HISTORY 643
C.2 ALTERNATIVE AXIOMS 645
C.3 SOME OF THE EARLY PROBLEMS 647
D M O D E L I NG OF R A N D O M N E SS IN E N G I N E E R I NG S Y S T E
M S: A S U M M A RY 651
D.L ELEMENTARY CONCEPTS 651
D.2 PROBABILISTIC MODELS 651
IMAGE 7
XIV CONTENTS
D.3 WHAT MODELS HAVE WE DEVELOPED? 653
D.4 WHAT TOOLS HAVE WE DEVELOPED? 653
D.5 MATHEMATICAL SUBTLETIES 654
D.6 WHAT CAN WE DO WITH A MODEL? 655
REFERENCES 657
INDEX 663
|
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| isbn | 0070674914 |
| language | English |
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| physical | XVIII, 676 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | WCB McGraw-Hill |
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| series2 | McGraw-Hill series in electrical and computer engineering Communications and signal processing |
| spelling | Viniotis, Yannis Verfasser aut Probability and random processes for electrical engineers Yannis Viniotis Boston [u.a.] WCB McGraw-Hill 1998 XVIII, 676 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in electrical and computer engineering Communications and signal processing Mathematik Electrical engineering Mathematics Probabilities Stochastic processes Elektrotechnik (DE-588)4014390-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Elektrotechnik (DE-588)4014390-9 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007967608&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Viniotis, Yannis Probability and random processes for electrical engineers Mathematik Electrical engineering Mathematics Probabilities Stochastic processes Elektrotechnik (DE-588)4014390-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4014390-9 (DE-588)4057630-9 |
| title | Probability and random processes for electrical engineers |
| title_auth | Probability and random processes for electrical engineers |
| title_exact_search | Probability and random processes for electrical engineers |
| title_full | Probability and random processes for electrical engineers Yannis Viniotis |
| title_fullStr | Probability and random processes for electrical engineers Yannis Viniotis |
| title_full_unstemmed | Probability and random processes for electrical engineers Yannis Viniotis |
| title_short | Probability and random processes for electrical engineers |
| title_sort | probability and random processes for electrical engineers |
| topic | Mathematik Electrical engineering Mathematics Probabilities Stochastic processes Elektrotechnik (DE-588)4014390-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Mathematik Electrical engineering Mathematics Probabilities Stochastic processes Elektrotechnik Stochastischer Prozess |
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