Probability: the science of uncertainty with applications to investments, insurance, and engineering
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I
American Mathematical Soc.
2001
|
| Schriftenreihe: | Pure and applied undergraduate texts
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Originally published: Pacific Grove, CA : Brooks/Cole, c2001 |
| Beschreibung: | XIII, 448 S. graph. Darst. |
| ISBN: | 9780821847923 |
Internformat
MARC
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| 245 | 1 | 0 | |a Probability |b the science of uncertainty with applications to investments, insurance, and engineering |c Michael A. Bean |
| 264 | 1 | |a Providence, R.I |b American Mathematical Soc. |c 2001 | |
| 300 | |a XIII, 448 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied undergraduate texts |v 6 | |
| 500 | |a Originally published: Pacific Grove, CA : Brooks/Cole, c2001 | ||
| 650 | 0 | 7 | |a Anwendung |0 (DE-588)4196864-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804139005332160512 |
|---|---|
| adam_text | Contents
Introduction
1.1
What is Probability?
1
1.2
How Is Uncertainty Quantified?
2
1.3
Probability in Engineering and the Sciences
5
1.4
What Is Actuarial Science?
6
1.5
What Is Financial Engineering?
9
1.6
Interpretations of Probability
11
1.7
Probability Modeling in Practice
13
1.8
Outline of This Book
14
1.9
Chapter Summary
15
1.10
Further Reading
16
1.11
Exercises
17
A Survey of Some Basic Concepts Through Examples
19
2.1
Payoff in a Simple Game
19
2.2
Choosing Between Payoffs
25
2.3
Future Lifetimes
36
2.4
Simple and Compound Growth
42
2.5
Chapter Summary
49
2.6
Exercises
51
¡X
CONTENTS
Classical Probability
57
3.1
The Formal Language of Classical Probability
58
3.2
Conditional Probability
64
3.3
The Law of Total Probability
68
3.4
Bayes
Theorem
72
3.5
Chapter Summary
75
3.6
Exercises
76
3.7
Appendix on Sets, Combinatorics, and Basic
Probability Rules
85
Random Variables and Probability Distributions
91
4.1
Definitions and Basic Properties
91
4.1.1
What Is a Random Variable?
91
4.1.2
What Is a Probability Distribution?
92
4.1.3
Types of Distributions
94
4.1.4
Probability Mass Functions
97
4.1.5
Probability Density Functions
97
4.1.6
Mixed Distributions
100
4.1.7
Equality and Equivalence of Random Variables
102
4.1.8
Random Vectors and
Divariate
Distributions
104
4.1.9
Dependence and Independence of Random Variables
113
4.1.10
The Law of Total Probability and
Bayes
Theorem
(Distributional Forms)
119
4.1.11
Arithmetic Operations on Random Variables
124
4.1.12
The Difference Between Sums and Mixtures
125
4.1.13
Exercises
126
4.2
Statistical Measures of Expectation, Variation, and Risk
130
4.2.1
Expectation
130
4.2.2
Deviation from Expectation
143
4.2.3
Higher Moments
149
4.2.4
Exercises
153
4.3
Alternative Ways of Specifying Probability Distributions
155
4.3.1
Moment and
Cumulant
Generating Functions
155
CONTENTS
xi
4.3.2
Survival and Hazard
Functions
167
4.3.3
Exercises
170
4.4
Chapter Summary
173
4.5
Additional Exercises
177
4.6
Appendix on Generalized Density Functions (Optional)
178
Special Discrete Distributions
186
5.1
The Binomial Distribution
187
5.2
The
Poisson
Distribution
195
5.3
The Negative Binomial Distribution
200
5.4
The Geometric Distribution
206
5.5
Exercises
209
Special Continuous Distributions
221
6.1
Special Continuous Distributions for Modeling
Uncertain Sizes
221
6.1.1
The Exponential Distribution
221
6.1.2
The Gamma Distribution
226
6.1.3
The Pareto Distribution
233
6.2
Special Continuous Distributions for Modeling Lifetimes
235
6.2.1
The Weibull Distribution
235
6.2.2
The DeMoivre Distribution
241
6.3
Other Special Distributions
245
6.3.1
The Normal Distribution
245
6.3.2
The
Lognormal
Distribution
256
6.3.3
The Beta Distribution
260
6.4
Exercises
265
Transformations
of Random Variables
280
7.1
Determining the Distribution of a Transformed
Random Variable
281
xii CONTENTS
7.2
Expectation of a Transformed Random Variable
289
7.3
Insurance Contracts with Caps,
Déductibles,
and Coinsurance (Optional)
297
7.4
Life Insurance and Annuity Contracts (Optional)
303
7.5
Reliability of Systems with Multiple Components
or Processes (Optional)
311
7.6
Trigonometric Transformations (Optional)
317
7.7
Exercises
319
8
Sums and Products of Random Variables
____________325
8.1
Techniques for Calculating the Distribution of a Sum
325
8.1.1
Using the Joint Density
326
8.1.2
Using the Law of Total Probability
331
8.1.3
Convolutions
336
8.2
Distributions of Products and Quotients
337
8.3
Expectations of Sums and Products
339
8.3.1
Formulas for the Expectation of a Sum or Product
339
8.3.2
The Cauchy-Schwarz Inequality
340
8.3.3
Covariance and Conelation
341
8.4
The Law of Large Numbers
345
8.4.1
Motivating Example: Premium Determination in Insurance
346
8.4.2
Statement and Proof of the Law
349
8.4.3
Some Misconceptions Surrounding the Law of Large Numbers
351
8.5
The Central Limit Theorem
352
8.6
Normal Power Approximations (Optional)
354
8.7
Exercises
356
9
Mixtures and Compound Distributions
_____________363
9.1
Definitions and Basic Properties
363
9.2
Some Important Examples of Mixtures Arising in
Insurance
366
9.3
Mean and Variance of a Mixture
373
CONTENTS xiii
9.4 Moment
Generating Function of a Mixture
378
9.5
Compound Distributions
379
9.5.1
General Formulas
380
9.5.2
Special Compound Distributions
382
9.6
Exercises
384
The
Markowitz
Investment Portfolio Selection Model
396
10.1
Portfolios of Two Securities
397
10.2
Portfolios of Two Risky Securities and a Risk-Free Asset
403
10.3
Portfolio Selection with Many Securities
409
10.4
The Capital Asset Pricing Model
411
10.5
Further Reading
414
10.6
Exercises
415
Appendixes
421
A The Gamma Function
421
В
The Incomplete Gamma Function
423
С
The Beta Function
428
D
The Incomplete Beta Function
429
E
The Standard Normal Distribution
430
F
Mathematica
Commands for Generating the
Graphs of Special Distributions
432
G
Elementary Financial Mathematics
434
Answers to Selected Exercises
437
Index
441
|
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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 |
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| discipline | Sprachwissenschaft Mathematik Literaturwissenschaft |
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| id | DE-604.BV023805599 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:37:12Z |
| institution | BVB |
| isbn | 9780821847923 |
| language | English |
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| publishDate | 2001 |
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| series2 | Pure and applied undergraduate texts |
| spelling | Bean, Michael A. 1964- Verfasser (DE-588)138208972 aut Probability the science of uncertainty with applications to investments, insurance, and engineering Michael A. Bean Providence, R.I American Mathematical Soc. 2001 XIII, 448 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied undergraduate texts 6 Originally published: Pacific Grove, CA : Brooks/Cole, c2001 Anwendung (DE-588)4196864-5 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Anwendung (DE-588)4196864-5 s DE-604 Pure and applied undergraduate texts 6 (DE-604)BV035489189 6 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017447774&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bean, Michael A. 1964- Probability the science of uncertainty with applications to investments, insurance, and engineering Pure and applied undergraduate texts Anwendung (DE-588)4196864-5 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4064324-4 |
| title | Probability the science of uncertainty with applications to investments, insurance, and engineering |
| title_auth | Probability the science of uncertainty with applications to investments, insurance, and engineering |
| title_exact_search | Probability the science of uncertainty with applications to investments, insurance, and engineering |
| title_full | Probability the science of uncertainty with applications to investments, insurance, and engineering Michael A. Bean |
| title_fullStr | Probability the science of uncertainty with applications to investments, insurance, and engineering Michael A. Bean |
| title_full_unstemmed | Probability the science of uncertainty with applications to investments, insurance, and engineering Michael A. Bean |
| title_short | Probability |
| title_sort | probability the science of uncertainty with applications to investments insurance and engineering |
| title_sub | the science of uncertainty with applications to investments, insurance, and engineering |
| topic | Anwendung (DE-588)4196864-5 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Anwendung Wahrscheinlichkeitsrechnung |
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