The pleasures of probability:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York u.a.
Springer
1996
|
| Ausgabe: | corr. 2. print. |
| Schriftenreihe: | Undergraduate texts in mathematics: Readings in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 235 - 237 |
| Beschreibung: | XV, 241 S. graph. Darst. |
| ISBN: | 038794415X |
Internformat
MARC
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| 100 | 1 | |a Isaac, Richard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The pleasures of probability |c Richard Isaac |
| 250 | |a corr. 2. print. | ||
| 264 | 1 | |a New York u.a. |b Springer |c 1996 | |
| 300 | |a XV, 241 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Undergraduate texts in mathematics: Readings in mathematics | |
| 500 | |a Literaturverz. S. 235 - 237 | ||
| 650 | 4 | |a Probabilities |v Problems, exercises, etc | |
| 650 | 0 | 7 | |a Wahrscheinlichkeitstheorie |0 (DE-588)4079013-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1807865402771898368 |
|---|---|
| adam_text |
CONTENTS
PREFACE
VII
1
CARS,
GOATS,
AND
SAMPLE
SPACES
1
1.1
GETTING
YOUR
GOAT
.
1
1.2
NUTSHELL
HISTORY
AND
PHILOSOPHY
LESSON
.
2
1.3
LET
THOSE
DICE
ROLL.
SAMPLE
SPACES
.
3
1.4
DISCRETE
SAMPLE
SPACES.
PROBABILITY
DISTRIBUTIONS
AND
SPACES
.
5
1.5
THE
CAR-GOAT
PROBLEM
SOLVED
.
8
1.6
EXERCISES
FOR
CHAPTER
1
.
11
2
HOW
TO
COUNT:
BIRTHDAYS
AND
LOTTERIES
13
2.1
COUNTING
YOUR
BIRTHDAYS
.
13
2.2
FOLLOWING
YOUR
DREAMS
IN
LOTTOLAND
.
18
2.3
EXERCISES
FOR
CHAPTER
2
.
20
3
CONDITIONAL
PROBABILITY:
FROM
KINGS
TO
PRISONERS
21
3.1
SOME
PROBABILITY
RULES.
CONDITIONAL
PROBABILITY
.
21
3.2
DOES
THE
KING
HAVE
A
SISTER?
.
23
3.3
THE
PRISONER
'
S
DILEMMA
.
24
3.4
ALL
ABOUT
URNS
.
27
3.5
EXERCISES
FOR
CHAPTER
3
.
29
XII
CONTENTS
4
THE
FORMULA
OF
THOMAS
BAYES
AND
OTHER
MATTERS
31
4.1
ON
BLOOD
TESTS
AND
BAYES
'
S
FORMULA
.
31
4.2
AN
URN
PROBLEM
.
34
4.3
LAPLACE
'
S
LAW
OF
SUCCESSION
.
36
4.4
SUBJECTIVE
PROBABILITY
.
37
4.5
QUESTIONS
OF
PATERNITY
.
39
4.6
EXERCISES
FOR
CHAPTER
4
.
40
5
THE
IDEA
OF
INDEPENDENCE,
WITH
APPLICATIONS
41
5.1
INDEPENDENCE
OF
EVENTS
.
41
5.2
WAITING
FOR
THE
FIRST
HEAD
TO
SHOW
.
44
5.3
ON
THE
LIKELIHOOD
OF
ALIEN
LIFE
.
46
5.4
THE
MONKEY
AT
THE
TYPEWRITER
.
48
5.5
RARE
EVENTS
DO
OCCUR
.
50
5.6
RARE
VERSUS
EXTRAORDINARY
EVENTS
.
51
5.7
EXERCISES
FOR
CHAPTER
5
.
52
6
A
LITTLE
BIT
ABOUT
GAMES
55
6.1
THE
PROBLEM
OF
POINTS
.
55
6.2
CRAPS
.
56
6.3
ROULETTE
.
57
6.4
WHAT
ARE
THE
ODDS?
.
58
6.5
EXERCISES
FOR
CHAPTER
6
.
58
7
RANDOM
VARIABLES,
EXPECTATIONS,
AND
MORE
ABOUT
GAMES
61
7.1
RANDOM
VARIABLES
.
61
7.2
THE
BINOMIAL
RANDOM
VARIABLE
.
63
7.3
THE
GAME
OF
CHUCK-A-LUCK
AND
DE
MATE
'
S
PROBLEM
OF
DICE
64
7.4
THE
EXPECTATION
OF
A
RANDOM
VARIABLE
.
65
7.5
FAIR
AND
UNFAIR
GAMES
.
68
7.6
GAMBLING
SYSTEMS
.
71
7.7
ADMINISTERING
A
BLOOD
TEST
.
73
7.8
EXERCISES
FOR
CHAPTER
7
.
75
8
BASEBALL
CARDS,
THE
LAW
OF
LARGE
NUMBERS,
AND
BAD
NEWS
FOR
GAMBLERS
77
8.1
THE
COUPON
COLLECTOR
'
S
PROBLEM
.
77
8.2
INDICATOR
VARIABLES
AND
THE
EXPECTATION
OF
A
BINOMIAL
VARIABLE
.
79
8.3
INDEPENDENT
RANDOM
VARIABLES
.
80
8.4
THE
COUPON
COLLECTOR
'
S
PROBLEM
SOLVED
.
80
8.5
THE
LAW
OF
LARGE
NUMBERS
.
82
8.6
THE
LAW
OF
LARGE
NUMBERS
AND
GAMBLING
.
85
8.7
A
GAMBLER
'
S
FALLACY
.
87
CONTENTS
XIII
8.8
THE
VARIANCE
OF
A
RANDOM
VARIABLE
.
87
8.8.1
APPENDIX
.
89
8.8.2
THE
VARIANCE
OF
THE
SUM
OF
INDEPENDENT
RANDOM
VARIABLES
.
90
8.8.3
THE
VARIANCE
OF
S
N
/N
.
91
8.9
EXERCISES
FOR
CHAPTER
8
.
92
9
FROM
TRAFFIC
TO
CHOCOLATE
CHIP
COOKIES
WITH
THE
POISSON
DISTRIBUTION
95
9.1
A
TRAFFIC
PROBLEM
.
95
9.2
THE
POISSON
AS
AN
APPROXIMATION
TO
THE
BINOMIAL
.
99
9.3
APPLICATIONS
OF
THE
POISSON
DISTRIBUTION
.
100
9.4
THE
POISSON
PROCESS
.
101
9.5
EXERCISES
FOR
CHAPTER
9
.
102
10
THE
DESPERATE
CASE
OF
THE
GAMBLER
'
S
RUIN
103
10.1
LET
'
S
GO
FOR
A
RANDOM
WALK
.
103
10.2
THE
GAMBLER
'
S
RUIN
PROBLEM
.
104
10.3
BOLD
PLAY
OR
TIMID
PLAY?
.
108
10.4
EXERCISES
FOR
CHAPTER
10
.
109
11
BREAKING
STICKS,
TOSSING
NEEDLES,
AND
MORE:
PROBABILITY
ON
CONTINUOUS
SAMPLE
SPACES
111
11.1
CHOOSING
A
NUMBER
AT
RANDOM
FROM
AN
INTERVAL
.
ILL
11.2
BUS
STOP
.
114
11.3
THE
EXPECTATION
OF
A
CONTINUOUS
RANDOM
VARIABLE
.
114
11.4
NORMAL
NUMBERS
.
116
11.5
BERTRAND
'
S
PARADOX
.
120
11.6
WHEN
DO
WE
HAVE
A
TRIANGLE?
.
121
11.7
BUFFON
'
S
NEEDLE
PROBLEM
.
122
11.8
EXERCISES
FOR
CHAPTER
11
.
124
12
NORMAL
DISTRIBUTIONS,
AND
ORDER
FROM
DIVERSITY
VIA
THE
CENTRAL
LIMIT
THEOREM
127
12.1
MAKING
SENSE
OF
SOME
DATA
.
127
12.2
THE
NORMAL
DISTRIBUTIONS
.
130
12.3
SOME
PLEASANT
PROPERTIES
OF
NORMAL
DISTRIBUTIONS
.
132
12.4
THE
CENTRAL
LIMIT
THEOREM
.
134
12.5
HOW
MANY
HEADS
DID
YOU
GET?
.
136
12.6
WHY
SO
MANY
QUANTITIES
MAY
BE
APPROXIMATELY
NORMAL
.
.
137
12.7
EXERCISES
FOR
CHAPTER
12
.
139
13
RANDOM
NUMBERS:
WHAT
THEY
ARE
AND
HOW
TO
USE
THEM
141
13.1
WHAT
ARE
RANDOM
NUMBERS?
.
141
XIV
CONTENTS
13.2
WHEN
ARE
DIGITS
RANDOM?
STATISTICAL
RANDOMNESS
.
145
13.3
PSEUDO-RANDOM
NUMBERS
.
147
13.4
RANDOM
SEQUENCES
ARISING
FROM
DECIMAL
EXPANSIONS
.
148
13.5
THE
USE
OF
RANDOM
NUMBERS
.
149
13.6
THE
1970
DRAFT
LOTTERY
.
153
13.7
EXERCISES
FOR
CHAPTER
13
.
155
14
COMPUTERS
AND
PROBABILITY
157
14.1
A
LITTLE
BIT
ABOUT
COMPUTERS
.
157
14.2
FREQUENCY
OF
ZEROS
IN
A
RANDOM
SEQUENCE
.
159
14.3
SIMULATION
OF
TOSSING
A
COIN
.
159
14.4
SIMULATION
OF
ROLLING
A
PAIR
OF
DICE
.
160
14.5
SIMULATION
OF
THE
BUFFON
NEEDLE
TOSSES
.
161
14.6
MONTE
CARLO
ESTIMATE
OF
TT
USING
BOMBARDMENT
OF
A
CIRCLE
.
161
14.7
MONTE
CARLO
ESTIMATE
FOR
THE
BROKEN
STICK
PROBLEM
.
162
14.8
MONTE
CARLO
ESTIMATE
OF
A
BINOMIAL
PROBABILITY
.
163
14.9
MONTE
CARLO
ESTIMATE
OF
THE
PROBABILITY
OF
WINNING
AT
CRAPS
.
164
14.10
MONTE
CARLO
ESTIMATE
OF
THE
GAMBLER
'
S
RUIN
PROBABILITY
.
.
165
14.11
CONSTRUCTING
APPROXIMATELY
NORMAL
RANDOM
VARIABLES
.
.
.
166
14.12
EXERCISES
FOR
CHAPTER
14
.
167
15
STATISTICS:
APPLYING
PROBABILITY
TO
MAKE
DECISIONS
169
15.1
WHAT
STATISTICS
DOES
.
169
15.2
LYING
WITH
STATISTICS?
.
170
15.3
DECIDING
BETWEEN
TWO
PROBABILITIES
.
171
15.4
MORE
COMPLICATED
DECISIONS
.
173
15.5
HOW
MANY
FISH
IN
THE
LAKE,
AND
OTHER
PROBLEMS
OF
ESTIMATION
.
176
15.6
POLLS
AND
CONFIDENCE
INTERVALS
.
180
15.7
RANDOM
SAMPLING
.
182
15.8
SOME
CONCLUDING
REMARKS
.
184
15.9
EXERCISES
FOR
CHAPTER
15
.
185
16
ROAMING
THE
NUMBER
LINE
WITH
A
MARKOV
CHAIN:
DEPENDENCE
187
16.1
A
PICNIC
IN
ALPHAVILLE?
.
187
16.2
ONE-DIMENSIONAL
RANDOM
WALKS
.
190
16.3
THE
PROBABILITY
OF
EVER
RETURNING
"
HOME
"
.
192
16.4
ABOUT
THE
GAMBLER
RECOUPING
HER
LOSSES
.
195
16.5
THE
DYING
OUT
OF
FAMILY
NAMES
.
197
16.6
THE
NUMBER
OF
PARTIES
WAITING
FOR
A
TAXI
.
.
198
16.7
STATIONARY
DISTRIBUTIONS
.
199
16.8
APPLICATIONS
TO
GENETICS
.
200
16.9
EXERCISES
FOR
CHAPTER
16
.
201
CONTENTS
XV
17
THE
BROWNIAN
MOTION,
AND
OTHER
PROCESSES
IN
CONTINUOUS
TIME
203
17.1
PROCESSES
IN
CONTINUOUS
TIME
.
203
17.2
A
FEW
COMPUTATIONS
FOR
THE
POISSON
PROCESS
.
206
17.3
THE
BROWNIAN
MOTION
PROCESS
.
206
17.4
A
FEW
COMPUTATIONS
FOR
BROWNIAN
MOTION
.
208
17.5
BROWNIAN
MOTION
AS
A
LIMIT
OF
RANDOM
WALKS
.
210
17.6
EXERCISES
FOR
CHAPTER
17
.
213
ANSWERS
TO
EXERCISES
215
BIBLIOGRAPHY
235
INDEX
239 |
| any_adam_object | 1 |
| author | Isaac, Richard |
| author_facet | Isaac, Richard |
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| author_sort | Isaac, Richard |
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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 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | corr. 2. print. |
| format | Book |
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| id | DE-604.BV011404355 |
| illustrated | Illustrated |
| indexdate | 2024-08-20T00:46:40Z |
| institution | BVB |
| isbn | 038794415X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007666933 |
| oclc_num | 47258781 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-703 |
| owner_facet | DE-91G DE-BY-TUM DE-703 |
| physical | XV, 241 S. graph. Darst. |
| publishDate | 1996 |
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| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics: Readings in mathematics |
| spelling | Isaac, Richard Verfasser aut The pleasures of probability Richard Isaac corr. 2. print. New York u.a. Springer 1996 XV, 241 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics: Readings in mathematics Literaturverz. S. 235 - 237 Probabilities Problems, exercises, etc Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007666933&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Isaac, Richard The pleasures of probability Probabilities Problems, exercises, etc Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4079013-7 |
| title | The pleasures of probability |
| title_auth | The pleasures of probability |
| title_exact_search | The pleasures of probability |
| title_full | The pleasures of probability Richard Isaac |
| title_fullStr | The pleasures of probability Richard Isaac |
| title_full_unstemmed | The pleasures of probability Richard Isaac |
| title_short | The pleasures of probability |
| title_sort | the pleasures of probability |
| topic | Probabilities Problems, exercises, etc Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Probabilities Problems, exercises, etc Wahrscheinlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007666933&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT isaacrichard thepleasuresofprobability |