Fundamentals of applied probability theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
McGraw-Hill
1967
|
| Series: | McGraw-Hill series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 283 S. |
| ISBN: | 0070178151 |
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| 245 | 1 | 0 | |a Fundamentals of applied probability theory |
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Record in the Search Index
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| adam_text | CONTENTS
Preface vii
Events, Sample Space, and Probability 1
1 1 A Brief Introduction to the Algebra of Events 2
1 2 Sample Spaces for Models of Experiments 5
1 3 Probability Measure and the Relative Likelihood of Events 10
1 4 Conditional Probability and Its Interpretation in Sample Space 13
1 5 Probability Trees for Sequential Experiments 16
1 6 The Independence of Events 17
1 7 Examples 19
1 8 Bayes Theorem 25
1 9 Enumeration in Event Space: Permutations and Combinations 27
xiv CONTENTS
2. Random Variables 41
2 1 Random Variables and Their Event Spaces 42
2 2 The Probability Mass Function 44
2 3 Compound Probability Mass Functions 46
2 4 Conditional Probability Mass Functions 48
2 5 Independence and Conditional Independence of Random Variables 51
2 6 Functions of Random Variables 52
2 7 Expectation and Conditional Expectation 53
2 8 Examples Involving Discrete Random Variables 57
2 9 A Brief Introduction to the Unit impulse Function 63
2 10 The Probability Density Function
for a Continuous Random Variable 64
2 11 Compound Probability Density Functions 69
2 12 Conditional Probability Density Functions 72
2 13 Independence and Expectation for Continuous Random Variables 74
2 14 Derived Probability Density Functions 74
2 15 Examples Involving Continuous Random Variables 78
3. Transforms and Some Applications to Sums of Independent
Random Variables 97
3 1 The s Transform 98
3 2 The z Transform 99
3 3 Moment generating Properties of the Transforms 100
3 4 Sums of Independent Random Variables; Convolution 103
3 5 The Transform of the PDF
for the Sum of Independent Random Variables 106
3 6 A Further Note on Sums of Independent Random Variables 107
3 7 Sum of a Random Number
of Independent Identically Distributed Random Variables 109
3 8 An Example, with Some Notes on Inverse Transforms 112
3 9 Where Do We Go from Here? 116
4. Some Basic Probabilistic Processes 123
4 1 The Bernoulli Process 124
4 2 Interarrival Times for a Bernoulli Process 126
4 3 Summary of the Bernoulli Process 129
4 4 An Example 130
4 5 The Poisson Process 133
4 6 Interarrival Times for the Poisson Process 137
4 7 Some Additional Properties of Poisson Processes
and Poisson Random Variables 139
4 8 Summary of the Poisson Process 140
4 9 Examples 142
CONTENTS XV
4 10 Renewal Processes 14g
4 11 Random Incidence 149
5. Discrete state Markov Processes 163
5 1 Series of Dependent Trials for Discrete state Processes 164
5 2 Discrete state Discrete transition Markov Processes 164
5 3 State Classification and the Concept of Limiting state Probabilities 167
5 4 The Ergodic Theorem 170
5 5 The Analysis of Discrete state Discrete transition Markov Processes 171
5 6 Examples Involving Discrete transition Markov Processes 175
5 7 Discrete state Continuous transition Markov Processes 180
5 8 Examples Involving Continuous transition Processes 185
6. Some Fundamental Limit Theorems 203
6 1 The Chebyshev Inequality 204
6 2 Stochastic Convergence 205
6 3 The Weak Law of Large Numbers 206
6 4 The Gaussian PDF 207
6 5 Central Limit Theorems 212
6 6 Approximations Based on the Central Limit Theorem 215
6 7 Using the Central Limit Theorem for the Binomial PMF 216
6 8 The Poisson Approximation to the Binomial PMF 219
6 9 A Note on Other Types of Convergence 220
7. An Introduction to Statistics 229
7 1 Statistics Is Different 230
7 2 Statistical Models and Some Related Issues 230
7 3 Statistics: Sample Values and Experimental Values 231
7 4 Significance Testing 234
7 5 Parametric and Nonparametric Hypotheses 239
7 6 Hypothesis Testing 240
7 7 Estimation 243
7 8 Some Properties of Desirable Estimators 245
7 9 Maximum likelihood Estimation 247
7 10 Bayesian Analysis 250
7 11 Complementary PDF s for Bayesian Analysis 253
7 12 Some Comments on Bayesian Analysis and Classical Statistics 255
Appendix 1. Further Reading 265
Appendix 2. Common PDF s, PMF s, and Their Means, Variances, and Transforms 271
Index 277
|
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| institution | BVB |
| isbn | 0070178151 |
| language | English |
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| series2 | McGraw-Hill series in probability and statistics |
| spelling | Drake, Alvin W. Verfasser aut Fundamentals of applied probability theory New York McGraw-Hill 1967 XV, 283 S. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in probability and statistics Probabilities Probability Theory Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002576266&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Drake, Alvin W. Fundamentals of applied probability theory Probabilities Probability Theory Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4151278-9 |
| title | Fundamentals of applied probability theory |
| title_auth | Fundamentals of applied probability theory |
| title_exact_search | Fundamentals of applied probability theory |
| title_full | Fundamentals of applied probability theory |
| title_fullStr | Fundamentals of applied probability theory |
| title_full_unstemmed | Fundamentals of applied probability theory |
| title_short | Fundamentals of applied probability theory |
| title_sort | fundamentals of applied probability theory |
| topic | Probabilities Probability Theory Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Probabilities Probability Theory Wahrscheinlichkeitsrechnung Einführung |
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