Probabilistic systems analysis: an introduction to probabilistic models, decisions, and applications of random processes
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1970
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 352 S. Illustrationen |
| ISBN: | 0471101818 |
Staff View
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| 245 | 1 | 0 | |a Probabilistic systems analysis |b an introduction to probabilistic models, decisions, and applications of random processes |c Arthur M. Breipohl |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1970 | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
I. INTRODUCTION
1 1 Variation 1
1 2 Probabilistic and deterministic models 2
II. ELEMENTARY PROBABILITY
2 1 What is probability 4
2 2 Elementary set theory 7
2 3 Sample space 17
2 4 Probability measure 18
2 5 Combined experiments 26
2 6 Independence 31
2 7 Bayes rule 34
2 8 Two useful models of sequential experiments 36
2 9 Summary 40
2 10 Problems 42
III. ENGINEERING APPLICATIONS OF PROBABILITY
3 1 Reliability 47
3 2 Elementary calculation of system success probability 48
3 3 Conditional probabilities in system reliability analysis 57
3 4 Summary of reliability calculations 62
3 5 Acceptance sampling 62
3 6 Summary 66
3 7 Problems 66
xi
CONTENTS
IV. RANDOM VARIABLES
4 1 The concept of a random variable 71
4 2 Distributions 75
4 3 Examples of distribution functions 78
4 4 Two random variables 86
4 5 Conditional distributions 91
4 6 Random vectors (n random variables) 97
4 7 Independent random variables 99
4 8 Summary 101
4 9 Problems 102
V. EXPECTED VALUES
5 1 Mean value 106
5 2 Variance 107
5 3 Expected value of functions of random variables 109
5 4 Properties of expected values 110
5 5 Examples of mean and variance 112
5 6 Characteristic function 115
5 7 Covariance and correlation 118
5 8 Conditional expectation 121
5 9 Summary 124
5 10 Problems 125
VI. DISTRIBUTION OF FUNCTIONS OF RANDOM
VARIABLES
6 1 Functions of one random variable 129
6 2 Sum of two random variables 139
6 3 Convolution 141
6 4 Characteristic function of the sum of random variables 145
6 5 Sum of n random variables 146
6 6 Distribution of Y = g(Xx, X2,... , XJ 150
xii
CONTENTS
6 7 Approximating the distribution of Y = g(Xu X2,..., Xn) 153
6 8 Synthetic sampling (Monte Carlo technique) 156
6 9 Summary 159
6 10 Problems 159
Vn. APPLICATIONS OF RANDOM VARIABLES TO
SYSTEM PROBLEMS
7 1 Introduction to sensitivity studies 163
7 2 Introduction to tolerance studies 168
7 3 Closure time of switching circuits 173
7 4 Introduction to time varying reliability studies 176
7 5 Problems 182
VIII. DISTRIBUTIONS FROM DATA
8 1 Bayes rule 186
8 2 Distribution of probability 188
8 3 Exponential situation 195
8 4 Normal situation 196
8 5 General comments on Bayesian statistics 199
8 6 Empirical distribution 201
8 7 Summary 205
8 8 Problems 208
IX. ESTIMATION
9 1 Parameter estimation 213
9 2 Good estimators 215
9 3 Methods of determining estimators 217
9 4 Moments of the empirical, distribution function 217
9 5 Estimates from Bayesian distributions 221
9 6 Maximum likelihood estimates 226
9 7 Indirect estimation 227
9 8 Linear mean square estimation 228
xiii
CONTENTS
9 9 Mean square estimation 233
9 10 Curve fitting or regression 235
9 11 Summary 238
9 12 Problems 238
X. ENGINEERING DECISIONS
10 1 Expected gain of a decision 242
10 2 Choosing among alternative designs 242
10 3 Detection of a signal in noise 245
10 4 Summary of probabilistic decision theory 248
10 5 Unknown probability distributions 252
10 6 Statistical decision theory 254
10 7 Empirical decision theory 256
10 8 Bayesian decision theory 258
10 9 Maximum amount to be spent on testing 264
10 10 The test decision 266
10 11 Summary 268
10 12 Problems 269
XI. INTRODUCTION TO RANDOM PROCESSES
11 1 General description 273
11 2 Examples of some special processes 278
11 3 Moments 282
11 4 Stationary processes 287
11 5 Normal processes 290
11 6 Time averages and ergodicity 291
11 7 Power density spectrum 296
11 8 Two random processes 302
11 9 Summary 304
11 10 Problems 304
xiv
CONTENTS
XII. SYSTEMS AND RANDOM SIGNALS
12 1 Operations on random processes 308
12 2 Differentiation of random process 313
12 3 Review of linear system analysis 316
12 4 Random process input to a linear system 321
12 5 Thermal noise 327
12 6 Summary 330
12 7 Problems 331
REFERENCES 337
ANSWERS TO SELECTED PROBLEMS 339
INDEX 349
xv
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| id | DE-604.BV005687913 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:33:09Z |
| institution | BVB |
| isbn | 0471101818 |
| language | English |
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| physical | XV, 352 S. Illustrationen |
| publishDate | 1970 |
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| publisher | Wiley |
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| spelling | Breipohl, Arthur M. Verfasser aut Probabilistic systems analysis an introduction to probabilistic models, decisions, and applications of random processes Arthur M. Breipohl New York [u.a.] Wiley 1970 XV, 352 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Mathématiques de l'ingénieur Probabilités Systèmes (Génie) Engineering mathematics Probabilities Systems engineering Systemtheorie (DE-588)4058812-9 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Systemtheorie (DE-588)4058812-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003552699&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Breipohl, Arthur M. Probabilistic systems analysis an introduction to probabilistic models, decisions, and applications of random processes Mathématiques de l'ingénieur Probabilités Systèmes (Génie) Engineering mathematics Probabilities Systems engineering Systemtheorie (DE-588)4058812-9 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4058812-9 (DE-588)4064324-4 |
| title | Probabilistic systems analysis an introduction to probabilistic models, decisions, and applications of random processes |
| title_auth | Probabilistic systems analysis an introduction to probabilistic models, decisions, and applications of random processes |
| title_exact_search | Probabilistic systems analysis an introduction to probabilistic models, decisions, and applications of random processes |
| title_full | Probabilistic systems analysis an introduction to probabilistic models, decisions, and applications of random processes Arthur M. Breipohl |
| title_fullStr | Probabilistic systems analysis an introduction to probabilistic models, decisions, and applications of random processes Arthur M. Breipohl |
| title_full_unstemmed | Probabilistic systems analysis an introduction to probabilistic models, decisions, and applications of random processes Arthur M. Breipohl |
| title_short | Probabilistic systems analysis |
| title_sort | probabilistic systems analysis an introduction to probabilistic models decisions and applications of random processes |
| title_sub | an introduction to probabilistic models, decisions, and applications of random processes |
| topic | Mathématiques de l'ingénieur Probabilités Systèmes (Génie) Engineering mathematics Probabilities Systems engineering Systemtheorie (DE-588)4058812-9 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Mathématiques de l'ingénieur Probabilités Systèmes (Génie) Engineering mathematics Probabilities Systems engineering Systemtheorie Wahrscheinlichkeitsrechnung |
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