Understanding probability:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | X, 562 S. Ill., graph. Darst. |
| ISBN: | 9781107658561 |
Internformat
MARC
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| 100 | 1 | |a Tijms, Henk C. |d 1944- |e Verfasser |0 (DE-588)114608474 |4 aut | |
| 245 | 1 | 0 | |a Understanding probability |c Henk Tijms |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2012 | |
| 300 | |a X, 562 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804149191769849856 |
|---|---|
| adam_text | Contents
Preface
page
ix
Introduction
1
PART ONE: PROBABILITY IN ACTION
9
1
Probability questions
11
2
Law of large numbers and simulation
18
2.1
Law of large numbers for probabilities
19
2.2
Basic probability concepts
28
2.3
Expected value and the law of large numbers
34
2.4
Drunkard s walk
38
2.5
St. Petersburg paradox
41
2.6
Roulette and the law of large numbers
44
2.7
Kelly betting system
46
2.8
Random-number generator
52
2.9
Simulating from probability distributions
57
2.10
Problems
65
3
Probabilities in everyday life
75
3.1
Birthday problem
76
3.2
Coupon collector s problem
83
3.3
Craps
86
3.4
Gambling systems for roulette
90
3.5
Gambler s ruin problem
93
3.6
Optimal stopping
95
vi
Contents
ЪЛ
The
1970
draft lottery
98
3.8
Problems
102
4
Rare events and lotteries
108
4.1
Binomial distribution
109
4.2
Poisson
distribution
111
4.3
Hypergeometric distribution
129
4.4
Problems
136
5
Probability and statistics
142
5.1
Normal curve
144
5.2
Concept of standard deviation
152
5.3
Square-root law
160
5.4
Central limit theorem
162
5.5
Graphical illustration of the central limit theorem
166
5.6
Statistical applications
168
5.7
Confidence intervals for simulations
171
5.8
Central limit theorem and random walks
177
5.9
Brownian motion
186
5.10
Falsified data and Benford s law
196
5.11
Normal distribution strikes again
202
5.12
Statistics and probability theory
203
5.13
Problems
206
6
Chance trees and
Bayes
rule
212
6.1
Monty Hall dilemma
213
6.2
Test paradox
218
6.3
Problems
222
PART TWO: ESSENTIALS OF PROBABILITY
227
7
Foundations of probability theory
229
7.1
Probabilistic foundations
230
7.2
Compound chance experiments
239
7.3
Some basic rules
243
8
Conditional probability and
Bayes
256
8.1
Conditional probability
256
8.2
Law of conditional probability
266
Contents
vii
8.3
Bayes
rule in odds form
270
8.4
Bayesian statistics
-
discrete case
278
9
Basic rules for discrete random variables
283
9.1
Random variables
283
9.2
Expected value
286
9.3
Expected value of sums of random variables
290
9.4
Substitution rule and variance
293
9.5
Independence of random variables
299
9.6
Important discrete random variables
303
10
Continuous random variables
318
10.1
Concept of probability density
319
10.2
Expected value of a continuous random
variable
326
10.3
Substitution rule and the variance
328
10.4
Important probability densities
333
10.5
Transformation of random variables
353
10.6
Failure rate function
357
11
Jointly distributed random variables
360
11.1
Joint probability mass function
360
11.2
Joint probability density function
362
11.3
Marginal probability densities
367
11.4
Transformation of random variables
374
11.5
Covariance and correlation coefficient
377
12
Multivariate normal distribution
382
12.1
Divariate
normal distribution
382
12.2
Multivariate normal distribution
391
12.3
Multidimensional central limit theorem
393
12.4
Chi-square test
399
13
Conditioning by random variables
404
13.1
Conditional distributions
404
13.2
Law of conditional probability for random variables
411
13.3
Law of conditional expectation
418
13.4
Conditional expectation as a computational tool
422
13.5
Bayesian statistics
—
continuous case
428
viii Contents
14
Generating functions
435
14.1
Generating functions
435
14.2
Moment-generating functions
443
14.3
Chernoff bound
448
14.4
Strong law of large numbers revisited
450
14.5
Central limit theorem revisited
454
14.6
Law of the iterated logarithm
456
15
Discrete-time Markov chains
459
15.1
Markov chain model
460
15.2
Time-dependent analysis of Markov chains
468
15.3
Absorbing Markov chains
472
15.4
Long-run analysis of Markov chains
481
15.5
Markov chain Monte Carlo simulation
490
16
Continuous-time Markov chains
507
16.1
Markov chain model
507
16.2
Time-dependent probabilities
516
16.3
Limiting probabilities
520
Appendix Counting methods and ex
532
Recommended reading
538
Answers to odd-numbered problems
539
Bibliography
556
Index
558
|
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| discipline | Informatik Mathematik |
| edition | 3. ed. |
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| isbn | 9781107658561 |
| language | English |
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| spelling | Tijms, Henk C. 1944- Verfasser (DE-588)114608474 aut Understanding probability Henk Tijms 3. ed. Cambridge [u.a.] Cambridge Univ. Press 2012 X, 562 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Analysis (DE-588)4001865-9 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Zufall (DE-588)4068050-2 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Analysis (DE-588)4001865-9 s Zufall (DE-588)4068050-2 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025050168&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tijms, Henk C. 1944- Understanding probability Analysis (DE-588)4001865-9 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Zufall (DE-588)4068050-2 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4064324-4 (DE-588)4068050-2 |
| title | Understanding probability |
| title_auth | Understanding probability |
| title_exact_search | Understanding probability |
| title_full | Understanding probability Henk Tijms |
| title_fullStr | Understanding probability Henk Tijms |
| title_full_unstemmed | Understanding probability Henk Tijms |
| title_short | Understanding probability |
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