Introduction to probability with R:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
Chapman & Hall/CRC
2008
|
| Schriftenreihe: | Texts in statistical science
75 |
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVI, 363 S. Ill., graph. Darst. |
| ISBN: | 1420065211 9781420065213 |
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| 245 | 1 | 0 | |a Introduction to probability with R |c Kenneth Baclawski |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b Chapman & Hall/CRC |c 2008 | |
| 300 | |a XVI, 363 S. |b Ill., graph. Darst. | ||
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| 490 | 1 | |a Texts in statistical science |v 75 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Probabilities | |
| 650 | 4 | |a R (Computer program language) |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804137338678280192 |
|---|---|
| adam_text | Contents
Foreword
xi
Preface
xiii
1
Sets, Events and Probability
1
1.1
The Algebra of Sets
2
1.2
The Bernoulli Sample Space
5
1.3
The Algebra of Multisets
7
1.4
The Concept of Probability
8
1.5
Properties of Probability Measure«
9
1.6
Independent Events
11
1.7
The Bernoulli Process
. 12
1.8
The
R
Language
14
1.9
Exercises
19
1.10
Answers to Selected Exercises
22
2
Finite Processes
29
2.1
The Basic Models
30
2.2
Counting Rules
31
2.3
Computing Factorials
32
2.4
The Second Rule of Counting
33
2.5
Computing Probabilities
35
2.6
Exercises
38
2.7
Answers to Selected Exercises
42
3
Discrete Random Variables
47
3.1
The Bernoulli Process: Tossing a Coin
49
3.2
The Bernoulli Process: Random Walk
61
3.3
Independence and Joint Distributions
02
3.4
Expectations
64
3.5
The Inclusion-Exclusion Principle
67
3.C Exercises
71
3.7
Answers to Selected Exercises
75
4
General Random Variables
87
4.1
Order Statistics
91
і
CONTENTS
4.2
The Concept of a General Random Variable
93
4.3
Joint
Distribution
and Joint Density
96
4.4
Mean, Median and Mode
97
4.5
The Uniform Process
98
4.6
Table of Probability Distributions
102
4.7
Scale
Invariance
104
4.8
Exercises
106
4.9
Answers to Selected Exercises 111
Statistics and the Normal Distribution
119
5.1
Variance
120
5.2
Bell-Shaped Curve
126
5.3
The Central Limit Theorem
128
5.4
Significance Levels
132
5.5
Confidence Intervals
134
5.6
The Law of Large Numbers
137
5.7
The Cauchy Distribution
139
5.8
Exercises
143
5.9
Answers to Selected Exercises
153
Conditional Probability
165
6.1
Discrete Conditional Probability
166
6.2
Gaps and Runs in the Bernoulli Process
170
6.3
Sequential Sampling
173
6.4
Continuous Conditional Probability
177
6.5
Conditional Densities
180
6.6
Gaps in the Uniform Process
182
6.7
The Algebra of Probability Distributions
186
6.8
Exercises
191
6.9
Answers to Selected Exercises
199
The
Poisson
Process
209
7.1
Continuous Waiting Times
209
7.2
Comparing Bernoulli with Uniform
215
7.3
The
Poisson
Sample Space
220
7.4
Consistency of the Poissou. Process
228
7.5
Exercises
229
7.6
Answers to Selected Exercises
235
Randomization and Compound Processes
241
8.1
Randomized Bernoulli Process
242
8.2
Randomized Uniform Process
243
8.3
Randomized
Poisson
Process
245
8.4
Laplace Transforms and Renewal Processes
247
8.5
Proof of the Central Limit Theorem
251
CONTENTS ix
8.6
Randomized Sampling
Processe«
252
8.7
Prior and Posterior Distributions
253
8.8
Reliability Theory
256
8.9
Bayesian Networks
259
8.10
Exercises
263
8.11
Answer« to Selected Exercises
266
9
Entropy and Information
275
9.1
Discrete Entropy
275
9.2
The Shannon Coding Theorem
282
9.3
Continuous Entropy
285
9.4
Proofs of Shannon s Theorems
292
9.5
Exercises
297
9.6
Answers to Selected Exercises
298
10
Markov Chains
303
10.1
The Markov Property
303
10.2
The Ruin Problem
Ж)7
10.3
The Network of a Markov Chain
312
10.4
The Evolution of a Markov Chain
31.4
10.5
The Markov Sample Space
318
10.6
Invariant Distributions
322
10.7
Monte Carlo Markov Chains
327
10.8
Exercise«
330
10.9
Answers to Selected Exercises
332
A Random Walks
343
A.I Fluctuations of Random Walks
343
A.
2
The Arcsine Law of Random Walks
347
В
Memorylessness and Scale-Invariance
351
B.I Memorylessnes.s
351
B.2 Self-Similarity
352
References
355
Index
357
|
| adam_txt |
Contents
Foreword
xi
Preface
xiii
1
Sets, Events and Probability
1
1.1
The Algebra of Sets
2
1.2
The Bernoulli Sample Space
5
1.3
The Algebra of Multisets
7
1.4
The Concept of Probability
8
1.5
Properties of Probability Measure«
9
1.6
Independent Events
11
1.7
The Bernoulli Process
. 12
1.8
The
R
Language
14
1.9
Exercises
19
1.10
Answers to Selected Exercises
22
2
Finite Processes
29
2.1
The Basic Models
30
2.2
Counting Rules
31
2.3
Computing Factorials
32
2.4
The Second Rule of Counting
33
2.5
Computing Probabilities
35
2.6
Exercises
38
2.7
Answers to Selected Exercises
42
3
Discrete Random Variables
47
3.1
The Bernoulli Process: Tossing a Coin
49
3.2
The Bernoulli Process: Random Walk
61
3.3
Independence and Joint Distributions
02
3.4
Expectations
64
3.5
The Inclusion-Exclusion Principle
67
3.C Exercises
71
3.7
Answers to Selected Exercises
75
4
General Random Variables
87
4.1
Order Statistics
91
і
CONTENTS
4.2
The Concept of a General Random Variable
93
4.3
Joint
Distribution
and Joint Density
96
4.4
Mean, Median and Mode
97
4.5
The Uniform Process
98
4.6
Table of Probability Distributions
102
4.7
Scale
Invariance
104
4.8
Exercises
106
4.9
Answers to Selected Exercises 111
Statistics and the Normal Distribution
119
5.1
Variance
120
5.2
Bell-Shaped Curve
126
5.3
The Central Limit Theorem
128
5.4
Significance Levels
132
5.5
Confidence Intervals
134
5.6
The Law of Large Numbers
137
5.7
The Cauchy Distribution
139
5.8
Exercises
143
5.9
Answers to Selected Exercises
153
Conditional Probability
165
6.1
Discrete Conditional Probability
166
6.2
Gaps and Runs in the Bernoulli Process
170
6.3
Sequential Sampling
173
6.4
Continuous Conditional Probability
177
6.5
Conditional Densities
180
6.6
Gaps in the Uniform Process
182
6.7
The Algebra of Probability Distributions
186
6.8
Exercises
191
6.9
Answers to Selected Exercises
199
The
Poisson
Process
209
7.1
Continuous Waiting Times
209
7.2
Comparing Bernoulli with Uniform
215
7.3
The
Poisson
Sample Space
220
7.4
Consistency of the Poissou. Process
228
7.5
Exercises
229
7.6
Answers to Selected Exercises
235
Randomization and Compound Processes
241
8.1
Randomized Bernoulli Process
242
8.2
Randomized Uniform Process
243
8.3
Randomized
Poisson
Process
245
8.4
Laplace Transforms and Renewal Processes
247
8.5
Proof of the Central Limit Theorem
251
CONTENTS ix
8.6
Randomized Sampling
Processe«
252
8.7
Prior and Posterior Distributions
253
8.8
Reliability Theory
256
8.9
Bayesian Networks
259
8.10
Exercises
263
8.11
Answer« to Selected Exercises
266
9
Entropy and Information
275
9.1
Discrete Entropy
275
9.2
The Shannon Coding Theorem
282
9.3
Continuous Entropy
285
9.4
Proofs of Shannon's Theorems
292
9.5
Exercises
297
9.6
Answers to Selected Exercises
298
10
Markov Chains
303
10.1
The Markov Property
303
10.2
The Ruin Problem
Ж)7
10.3
The Network of a Markov Chain
312
10.4
The Evolution of a Markov Chain
31.4
10.5
The Markov Sample Space
318
10.6
Invariant Distributions
322
10.7
Monte Carlo Markov Chains
327
10.8
Exercise«
330
10.9
Answers to Selected Exercises
332
A Random Walks
343
A.I Fluctuations of Random Walks
343
A.
2
The Arcsine Law of Random Walks
347
В
Memorylessness and Scale-Invariance
351
B.I Memorylessnes.s
351
B.2 Self-Similarity
352
References
355
Index
357 |
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| index_date | 2024-07-02T19:39:50Z |
| indexdate | 2024-07-09T21:10:43Z |
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| isbn | 1420065211 9781420065213 |
| language | English |
| lccn | 2007041288 |
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| series2 | Texts in statistical science |
| spelling | Baclawski, Kenneth Verfasser (DE-588)1065008619 aut Introduction to probability with R Kenneth Baclawski Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2008 XVI, 363 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in statistical science 75 Includes bibliographical references and index Mathematisches Modell Probabilities R (Computer program language) Mathematical models Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content R Programm (DE-588)4705956-4 s Stochastisches Modell (DE-588)4057633-4 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s b DE-604 Texts in statistical science 75 (DE-604)BV022819715 75 http://www.loc.gov/catdir/enhancements/fy0803/2007041288-d.html Publisher description Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016290528&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baclawski, Kenneth Introduction to probability with R Texts in statistical science Mathematisches Modell Probabilities R (Computer program language) Mathematical models Stochastisches Modell (DE-588)4057633-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd R Programm (DE-588)4705956-4 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4079013-7 (DE-588)4705956-4 (DE-588)4123623-3 |
| title | Introduction to probability with R |
| title_auth | Introduction to probability with R |
| title_exact_search | Introduction to probability with R |
| title_exact_search_txtP | Introduction to probability with R |
| title_full | Introduction to probability with R Kenneth Baclawski |
| title_fullStr | Introduction to probability with R Kenneth Baclawski |
| title_full_unstemmed | Introduction to probability with R Kenneth Baclawski |
| title_short | Introduction to probability with R |
| title_sort | introduction to probability with r |
| topic | Mathematisches Modell Probabilities R (Computer program language) Mathematical models Stochastisches Modell (DE-588)4057633-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd R Programm (DE-588)4705956-4 gnd |
| topic_facet | Mathematisches Modell Probabilities R (Computer program language) Mathematical models Stochastisches Modell Wahrscheinlichkeitstheorie R Programm Lehrbuch |
| url | http://www.loc.gov/catdir/enhancements/fy0803/2007041288-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016290528&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022819715 |
| work_keys_str_mv | AT baclawskikenneth introductiontoprobabilitywithr |