Introduction to probability and statistics for engineers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
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| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | X, 181 S. Ill., graph. Darst. |
| ISBN: | 3642382991 9783642382994 |
Internformat
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Datensatz im Suchindex
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CONTENTS
1 INTRODUCTION 1
REFERENCES 4
2 BASIC CONCEPTS OF PROBABILITY 5
2.1 EXPERIMENT, RANDOM EVENT, SAMPLE SPACE 5
2.1.1 EXPERIMENT 6
2.1.2 RANDOM EVENT 6
2.1.3 SAMPLE SPACE 7
2.2 RELATIONS BETWEEN RANDOM EVENTS 9
2.3 DEFINITIONS OF PROBABILITY 12
2.3.1 CLASSICAL DEFINITION 12
2.3.2 GEOMETRICAL DEFINITION 13
2.3.3 STATISTICAL DEFINITION 13
2.3.4 AXIOMATIC DEFINITION 13
2.4 BASIC RULES FOR THE COMPUTATION OF PROBABILITIES 15
2.5 CONDITIONAL PROBABILITY 16
2.6 BAYES'THEOREM 17
2.7 PROBABILITY UPDATING 19
2.8 BAYESIAN NETWORKS 22
2.9 NOTES ON THE FUZZY CONCEPT 25
REFERENCES 27
3 EVALUATION OF STATISTICAL DATA 29
3.1 POPULATION AND RANDOM SAMPLE 29
3.2 CHARACTERISTICS OF LOCATION 30
3.3 CHARACTERISTICS OF DISPERSION 30
3.4 CHARACTERISTICS OF ASYMMETRY AND KURTOSIS 32
3.5 GENERAL AND CENTRAL MOMENTS 33
3.6 COMBINATION OF TWO RANDOM SAMPLES 34
3.7 NOTE ON TERMINOLOGY AND SOFTWARE PRODUCTS 38
3.8 GROUPED DATA, HISTOGRAM 39
REFERENCES 41
HTTP://D-NB.INFO/1033706310
VIII CONTENTS
4 DISTRIBUTIONS OF RANDOM VARIABLES 43
4.1 RANDOM VARIABLES 43
4.2 DISTRIBUTION FUNCTION 44
4.3 DISCRETE RANDOM VARIABLES 44
4.4 CONTINUOUS RANDOM VARIABLES 45
4.5 PARAMETERS OF RANDOM VARIABLES 47
4.6 STANDARDIZED RANDOM VARIABLE 50
REFERENCES 52
5 SELECTED MODELS OF DISCRETE VARIABLES 53
5.1 ALTERNATIVE DISTRIBUTION 53
5.2 BINOMIAL DISTRIBUTION 54
5.3 HYPERGEOMETRIC DISTRIBUTION 56
5.4 POISSON DISTRIBUTION 58
5.5 GEOMETRIC DISTRIBUTION 59
REFERENCES 62
6 SELECTED MODELS OF CONTINUOUS VARIABLES 63
6.1 NORMAL DISTRIBUTION 63
6.2 LOGNORMAL DISTRIBUTION 65
6.3 GAMMA DISTRIBUTION 68
6.4 BETA DISTRIBUTION 69
6.5 GUMBEL DISTRIBUTION 73
6.6 BASIC RULES FOR SELECTING DISTRIBUTION 75
REFERENCES 78
7 FUNCTIONS OF RANDOM VARIABLES 79
7.1 FUNCTION OF A SINGLE RANDOM VARIABLE 79
7.2 FUNCTION OF TWO RANDOM VARIABLES 81
7.3 PARAMETERS OF FUNCTIONS OF INDEPENDENT RANDOM VARIABLES . . 83
7.4 PARAMETERS OF FUNCTIONS OF DEPENDENT RANDOM VARIABLES 85
7.5 UPDATING OF PROBABILITY DISTRIBUTIONS 86
7.6 CENTRAL LIMIT THEOREM 87
7.7 EXTREME VALUE DISTRIBUTION 91
REFERENCES 93
8 ESTIMATIONS OF POPULATION PARAMETERS 95
8.1 SAMPLING DISTRIBUTIONS 95
8.1.1 ^-DISTRIBUTION 96
8.1.2 R-DISTRIBUTION 97
8.1.3 F-DISTRIBUTION 98
8.2 POINT ESTIMATE OF THE MEAN 99
8.3 POINT ESTIMATE OF THE VARIANCE 100
8.4 INTERVAL ESTIMATE OF THE MEAN 101
8.4.1 KNOWN A 101
8.4.2 UNKNOWN A 102
CONTENTS IX
8.5 INTERVAL ESTIMATE OF THE VARIANCE 103
8.6 SPECIFICATION OF THE SAMPLE SIZE 103
8.6.1 KNOWN A 104
8.6.2 UNKNOWNS 104
8.7 ESTIMATION OF THE SKEWNESS 105
REFERENCES 107
9 FRACTILES OF RANDOM VARIABLES 109
9.1 FRACTILES OF THEORETICAL MODELS 109
9.2 FRACTILE ESTIMATION FROM SAMPLES: COVERAGE METHOD 115
9.3 FRACTILE ESTIMATION FROM SAMPLES: PREDICTION METHOD 116
9.4 COMPARISON OF THE COVERAGE AND PREDICTION METHODS 117
9.5 BAYESIAN ESTIMATION OF FRACTILES 121
REFERENCES 123
10 TESTING OF STATISTICAL HYPOTHESES 125
10.1 STATISTICAL TESTS 125
10.2 DEVIATION OF SAMPLE MEAN FROM POPULATION MEAN 127
10.2.1 KNOWN STANDARD DEVIATION 127
10.2.2 UNKNOWN STANDARD DEVIATION 128
10.3 DEVIATION OF SAMPLE VARIANCE FROM POPULATION VARIANCE 129
10.4 DIFFERENCE BETWEEN TWO SAMPLE MEANS 129
10.4.1 VARIANCES ARE KNOWN 130
10.4.2 VARIANCES ARE UNKNOWN 130
10.5 DIFFERENCE BETWEEN TWO SAMPLE VARIANCES 131
10.6 TESTS OF GOOD FIT 132
10.7 TESTS OF OUTLIERS 135
10.7.1 GRUBBSTEST 135
10.7.2 DIXON TEST 137
REFERENCES 138
11 CORRELATION AND REGRESSION 139
11.1 TWO-DIMENSIONAL RANDOM VARIABLES 139
11.2 TWO-DIMENSIONAL NORMAL DISTRIBUTION 141
11.3 TWO-DIMENSIONAL SAMPLES 142
11.4 REGRESSION LINES 144
11.5 ESTIMATION OF THE COEFFICIENT OF CORRELATION 145
11.6 ESTIMATION OF THE COEFFICIENTS OF REGRESSION 147
11.7 BOUNDARIES OF THE REGRESSION LINE 149
11.8 TESTS OF CORRELATION COEFFICIENT 149
11.9 TESTS OF REGRESSION COEFFICIENTS 151
REFERENCES 152
12 RANDOM FUNCTIONS 153
12.1 BASIC CONCEPTS 153
12.2 PARAMETERS OF RANDOM FUNCTION 154
X CONTENTS
12.3 CORRELATION FUNCTION 155
12.4 STATIONARY RANDOM FUNCTIONS 158
12.5 ERGODIC RANDOM FUNCTIONS 159
12.6 SPECTRAL REPRESENTATION OF RANDOM FUNCTIONS 161
REFERENCES 164
APPENDIX 1: SAMPLE CHARACTERISTICS AND POPULATION PARAMETERS 165
APPENDIX 2: THEORETICAL MODELS OF DISCRETE RANDOM VARIABLES 167
APPENDIX 3: THEORETICAL MODELS OF CONTINUOUS RANDOM VARIABLES . . . 169
APPENDIX 4: FUNCTIONS OF INDEPENDENT RANDOM VARIABLES 171
APPENDIX 5: FRACTILES OF RANDOM VARIABLES 173
APPENDIX 6: CONVENTIONAL PROBABILISTIC MODELS 175
APPENDIX 7: STANDARDIZED NORMAL DISTRIBUTION 179
BRIEF BIOGRAPHICAL NOTES 181 |
| any_adam_object | 1 |
| author | Holický, Milan |
| author_facet | Holický, Milan |
| author_role | aut |
| author_sort | Holický, Milan |
| author_variant | m h mh |
| building | Verbundindex |
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| 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 | Allgemeine Naturwissenschaft Mathematik |
| format | Book |
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| isbn | 3642382991 9783642382994 |
| language | English |
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| spelling | Holický, Milan Verfasser aut Introduction to probability and statistics for engineers Milan Holický Berlin [u.a.] Springer 2013 X, 181 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Statistik (DE-588)4056995-0 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-38300-7 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4301385&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026749660&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holický, Milan Introduction to probability and statistics for engineers Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4056995-0 |
| title | Introduction to probability and statistics for engineers |
| title_auth | Introduction to probability and statistics for engineers |
| title_exact_search | Introduction to probability and statistics for engineers |
| title_full | Introduction to probability and statistics for engineers Milan Holický |
| title_fullStr | Introduction to probability and statistics for engineers Milan Holický |
| title_full_unstemmed | Introduction to probability and statistics for engineers Milan Holický |
| title_short | Introduction to probability and statistics for engineers |
| title_sort | introduction to probability and statistics for engineers |
| topic | Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Wahrscheinlichkeitstheorie Statistik |
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