Problems and snapshots from the world of probability:
A wide range of readers will enjoy this diverse selection of topics. Students will find this a helpful and stimulating companion to their probability courses. The snapshots will leave the students with an expanded knowledge about topics not generally covered by textbooks. Other than a basic exposure...
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1994
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006040549&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Summary: | A wide range of readers will enjoy this diverse selection of topics. Students will find this a helpful and stimulating companion to their probability courses. The snapshots will leave the students with an expanded knowledge about topics not generally covered by textbooks. Other than a basic exposure to probabilistic ideas, such as might be gained from a first course in probability, it is self-contained Consequently, almost all of the problems can be tackled by undergraduate students as well as appeal to those who enjoy the challenge of constructing and solving problems |
| Abstract: | This book comprises a collection of 125 problems and snapshots from discrete probability. The problems are selected on the basis of their elegance and utility whereas the snapshots are intended to provide a quick overview of topics in probability. These include combinatorics, Poisson approximation, patterns in random sequences, Markov chains, random walks, cover times, and embedding procedures |
| Item Description: | Literaturverz. S. 230 - 235 |
| Physical Description: | XII, 240 S. Illustrationen |
| ISBN: | 3540941614 0387941614 |
Staff View
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| 245 | 1 | 0 | |a Problems and snapshots from the world of probability |c Gunnar Blom ; Lars Holst ; Dennis Sandell |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1994 | |
| 300 | |a XII, 240 S. |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Literaturverz. S. 230 - 235 | ||
| 520 | 3 | |a This book comprises a collection of 125 problems and snapshots from discrete probability. The problems are selected on the basis of their elegance and utility whereas the snapshots are intended to provide a quick overview of topics in probability. These include combinatorics, Poisson approximation, patterns in random sequences, Markov chains, random walks, cover times, and embedding procedures | |
| 520 | |a A wide range of readers will enjoy this diverse selection of topics. Students will find this a helpful and stimulating companion to their probability courses. The snapshots will leave the students with an expanded knowledge about topics not generally covered by textbooks. Other than a basic exposure to probabilistic ideas, such as might be gained from a first course in probability, it is self-contained | ||
| 520 | |a Consequently, almost all of the problems can be tackled by undergraduate students as well as appeal to those who enjoy the challenge of constructing and solving problems | ||
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Record in the Search Index
| DE-BY-TUM_call_number | 0102 MAT 600f 2001 A 7949 |
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| adam_text | Contents
Preface v
Symbols and formulas xi
1. Welcoming problems 1
1.1 The friendly illiterate 1
1.2 Tourist with a short memory 2
1.3 The car and the goats 3
1.4 Patterns I 4
1.5 Classical random walk I 6
1.6 Number of walks until no shoes 8
1.7 Banach s match box problem 9
1.8 The generous king 11
2. Basic probability theory I 13
2.1 Remarkable conditional probabilities 13
2.2 Exchangeability I 15
2.3 Exchangeability II 16
2.4 Combinations of events I 17
2.5 Problems concerning random numbers 19
2.6 Zero one random variables I 20
3. Basic probability theory II 23
3.1 A trick for determining expectations 23
3.2 Probability generating functions 24
3.3 People at the corners of a triangle 26
3.4 Factorial generating functions 27
3.5 Zero one random variables II 28
3.6 Combinations of events II 31
4. Topics from early days I 33
4.1 Cardano a pioneer 33
4.2 Birth of probability 34
4.3 The division problem 36
4.4 Huygens s second problem 37
4.5 Huygens s fifth problem 38
4.6 Points when throwing several dice 39
4.7 Bernoulli and the game of tennis 41
5. Topics from early days II 44
5.1 History of some common distributions 44
5.2 Waldegrave s problem I 47
5.3 Petersburg paradox 49
viii Contents
5.4 Rencontre I 50
5.5 Occupancy I 51
5.6 Stirling numbers of the second kind 54
5.7 Bayes s theorem and Law of Succession 56
5.8 Menage I 59
6. Random permutations 62
6.1 Runs I 62
6.2 Cycles in permutations 65
6.3 Stirling numbers of the first kind 67
6.4 Ascents in permutations 69
6.5 Eulerian numbers 70
6.6 Exceedances in permutations 71
6.7 Price fluctuations 72
6.8 Oscillations I 73
6.9 Oscillations II 76
7. Miscellaneous I 79
7.1 Birthdays 79
7.2 Poker 80
7.3 Negative binomial 82
7.4 Negative hypergeometric I 83
7.5 Coupon collecting I 85
7.6 Coupon collecting II 87
7.7 Menage II 88
7.8 Rencontre II 90
8. Poisson approximation 92
8.1 Similar pairs and triplets 92
8.2 A Lotto problem 94
8.3 Variation distance 94
8.4 Poisson binomial 96
8.5 Rencontre III 98
8.6 Menage III 99
8.7 Occupancy II 101
9. Miscellaneous II 103
9.1 Birthdays and similar triplets 103
9.2 Comparison of random numbers 105
9.3 Grouping by random division 106
9.4 Records I 108
9.5 Records II 110
9.6 A modification of blackjack 112
10. Random walks 115
10.1 Introduction 115
10.2 Classical random walk II 117
Contents ix
10.3 One absorbing barrier 119
10.4 The irresolute spider 121
10.5 Stars I 122
10.6 Closed stopping region 123
10.7 The reflection principle 125
10.8 Ballot problem 128
10.9 Range of a random walk 130
11. Urn models 133
11.1 Randomly filled urn 133
11.2 Polya s model I 135
11.3 Polya s model II 136
11.4 Polya s model III 137
11.5 Ehrenfest s model I 140
11.6 Ehrenfest s game 142
11.7 A pill problem 143
12. Cover times 146
12.1 Introduction 146
12.2 Complete graph 149
12.3 Linear finite graph 149
12.4 Polygon 150
12.5 A false conjecture 152
12.6 Stars II 153
12.7 Inequality for cover times 155
13. Markov chains 156
13.1 Review I 156
13.2 Review II 158
13.3 Random walk: two reflecting barriers 161
13.4 Ehrenfest s model II 162
13.5 Doubly stochastic transition matrix 163
13.6 Card shuffling 165
13.7 Transition times for Markov chains 167
13.8 Reversible Markov chains 169
13.9 Markov chains with homesickness 170
14. Patterns 173
14.1 Runs II 173
14.2 Patterns II 175
14.3 Patterns III 176
14.4 A game for pirates 178
14.5 Penney s game 179
14.6 Waldegrave s problem II 181
14.7 How many patterns? 181
x Contents
15. Embedding procedures 186
15.1 Drawings with replacement 186
15.2 Repetition of colours 189
15.3 Birthdays revisited 190
15.4 Coupon collecting III 191
15.5 Drawings without replacement 192
15.6 Socks in the laundry 193
15.7 Negative hypergeometric II 194
15.8 The first to r game I 195
16. Special topics 199
16.1 Exchangeability III 199
16.2 Martingales 201
16.3 Wald s equation 203
16.4 Birth control 204
16.5 The r heads in advance game 205
16.6 Patterns IV 207
16.7 Random permutation of l s and ( l) s 210
17. Farewell problems 214
17.1 The first to r game II 214
17.2 Random walk on a chessboard 216
17.3 Game with disaster 217
17.4 A rendezvous problem 219
17.5 Modified coin tossing 222
17.6 Palindromes 224
References 230
Index 236
|
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV009110277 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:32:23Z |
| institution | BVB |
| isbn | 3540941614 0387941614 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006040549 |
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| physical | XII, 240 S. Illustrationen |
| publishDate | 1994 |
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| publisher | Springer |
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| spellingShingle | Blom, Gunnar 1930- Holst, Lars Sandell, Dennis Problems and snapshots from the world of probability Waarschijnlijkheidstheorie gtt Probabilities Problems, exercises, etc Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4137007-7 (DE-588)4144384-6 |
| title | Problems and snapshots from the world of probability |
| title_auth | Problems and snapshots from the world of probability |
| title_exact_search | Problems and snapshots from the world of probability |
| title_full | Problems and snapshots from the world of probability Gunnar Blom ; Lars Holst ; Dennis Sandell |
| title_fullStr | Problems and snapshots from the world of probability Gunnar Blom ; Lars Holst ; Dennis Sandell |
| title_full_unstemmed | Problems and snapshots from the world of probability Gunnar Blom ; Lars Holst ; Dennis Sandell |
| title_short | Problems and snapshots from the world of probability |
| title_sort | problems and snapshots from the world of probability |
| topic | Waarschijnlijkheidstheorie gtt Probabilities Problems, exercises, etc Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd |
| topic_facet | Waarschijnlijkheidstheorie Probabilities Problems, exercises, etc Wahrscheinlichkeitsrechnung Wahrscheinlichkeit Beispielsammlung |
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| work_keys_str_mv | AT blomgunnar problemsandsnapshotsfromtheworldofprobability AT holstlars problemsandsnapshotsfromtheworldofprobability AT sandelldennis problemsandsnapshotsfromtheworldofprobability |
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Branch Library Mathematics & Informatics
| Call Number: |
0102 MAT 600f 2001 A 7949
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| Copy 1 | Available for loan On Shelf |