Introduction to finite probability:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Columbus, Ohio
Merrill
1967
|
| Series: | Merrill's mathematics and quantitative methods series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV,145 S. |
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MARC
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| 490 | 0 | |a Merrill's mathematics and quantitative methods series | |
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Record in the Search Index
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| adam_text | Contents
Part 1. Introduction to Probability
in Finite Sample Space 1
Chapter 1. Concepts of Probability
in Finite Sample Space 3
1 1. The Classical Concept — Equiprobable
Events 4
1 2. The Relative Frequency Concept —
Empirical Probability 6
1 3. Subjective Probabilities 8
1 4. Probability and Set Theory 9
Concepts to Think about 9
Selected References 10
Chapter 2. Fundamental Theorems of Probability 11
2 1. Some Basic Concepts 11
2 2. The Nature of Probability 12
2 3. Counting Schemes 13
2 4. Probabilities of Mutually Exclusive
Events 20
2 5. Union of Events in General 24
2 6. Independence and the Intersection
of Events 27
2 7. Nonindependence and Conditional
Probability 29
2 8. Bayes Formula 34
Exercises 38
Selected References 43
ix
Chapter 3. Finite Stochastic Processes 44
3—1. Outcomes of Sequences of
Experiments 44
3 2. Introduction of Finite Markov
Processes 50
3 3. Monte Carlo Simulation 56
Exercises 59
Selected References 61
Part 2. Distributions of
Discrete Random Variables 63
Chapter 4. Discrete Random Variables
and Expectation 65
4 1. Basic Concepts 65
4—2. Mathematical Expectation 68
4 3. Expected Value and Fair Games 71
4—4. The Mean and Variance of a Random
Variable 74
4 5. The Theorem of Tchebysheff 78
4 6. A Decision Problem 80
Exercises 85
Selected References 87
Chapter 5. Probability of a Sample from a
Finite Two Valued Set —the
Hypergeometric Distribution 88
5—1. Derivation of the Distribution 88
5 2. An Iterative Computational Formula 92
5 3. The Expected Value of X 93
5 4. The Variance of X 94
5 5. Extension to Sets of More than
Two Values 97
Exercises 98
Selected References 99
Chapter 6. Independent Trials with Two
Outcomes—the Binomial Distribution 100
6 1. Derivation of the Binomial Density
Function 100
6 2. General Characteristics of the
Distribution 103
6 3. The Expected Value of X 104
x
6 4. The Variance of X 106
6 5. Relation of the Binomial and Hypergeometric
Distributions 108
6 6. The Law of Large Numbers (Bernoulli s
Theorem) 111
6 7. Extension to the Multinomial
Distribution 112
6 8. Extension to the Pascal Distribution 113
Exercises 114
Selected References 116
Chapter 7. Discrete Random Variables in Time
or Space —the Poisson Distribution 117
7 1. Definition of the Distribution 117
7 2. Expected Value of X 120
7 3. Variance of X 120
7 4. Summary of Discrete Probability
Distributions 121
Exercises 123
Selected References 124
Chapter 8. Some Applications of Probability Theory
to Business and Related Problems 125
8 1. Inventory Control 126
8 2. Waiting Lines 127
8 3. Equipment Maintenance and
Replacement 128
8 4. Industrial Quality Control 128
8 5. Statistical Applications 129
8 6. Allowance for Bad Debts among
Department Store Accounts 130
8 7. Some Other Applications 130
8 8. Some Concluding Cemments 131
Selected References 132
Appendix 135
Table I. Combinatorial Values 135
Table II. Binomial Probabilities 136
Table III. Values of the
Exponential Function 142
Index 143
xi
|
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| id | DE-604.BV007040596 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:54:21Z |
| institution | BVB |
| language | English |
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| physical | XIV,145 S. |
| publishDate | 1967 |
| publishDateSearch | 1967 |
| publishDateSort | 1967 |
| publisher | Merrill |
| record_format | marc |
| series2 | Merrill's mathematics and quantitative methods series |
| spelling | Burford, Roger L. Verfasser aut Introduction to finite probability Roger L. Burford Columbus, Ohio Merrill 1967 XIV,145 S. txt rdacontent n rdamedia nc rdacarrier Merrill's mathematics and quantitative methods series Probabilités Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf 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=004466758&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burford, Roger L. Introduction to finite probability Probabilités Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4064324-4 |
| title | Introduction to finite probability |
| title_auth | Introduction to finite probability |
| title_exact_search | Introduction to finite probability |
| title_full | Introduction to finite probability Roger L. Burford |
| title_fullStr | Introduction to finite probability Roger L. Burford |
| title_full_unstemmed | Introduction to finite probability Roger L. Burford |
| title_short | Introduction to finite probability |
| title_sort | introduction to finite probability |
| topic | Probabilités Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Probabilités Probabilities Wahrscheinlichkeitsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004466758&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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