An edition of A natural introduction to probability theory
(2003)
A natural introduction to probability theory
Second
by Meester· Ronald.
Share
×Close
This edition doesn't have a description yet. Can you add one?
Buy this book
| Edition | Availability |
|---|---|
1
|
aaaa
|
2
|
zzzz
|
|
3
A natural introduction to probability theory
2003, Birkhauser·
in English
- First edition
0817621881 9780817621889
|
zzzz
|
Book Details
Table of Contents
.
Contents
Preface to the First Edition viii
Preface to the Second Edition x
1 Experiments 1
1.1 Definitions and Examples . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Counting and Combinatorics . . . . . . . . . . . . . . . . . . . . . 6
1.3 Properties of Probability Measures . . . . . . . . . . . . . . . . . . 10
1.4 Conditional Probabilities . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.6 A First Law of Large Numbers . . . . . . . . . . . . . . . . . . . . 26
1.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2 Random Variables and Random Vectors 35
2.1 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.3 Expectation and Variance . . . . . . . . . . . . . . . . . . . . . . . 43
2.4 Random Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.5 Conditional Distributions and Expectations . . . . . . . . . . . . . 57
2.6 Generating Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3 Random Walk 71
3.1 Random Walk and Counting . . . . . . . . . . . . . . . . . . . . . 71
3.2 The Arc-Sine Law . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4 Limit Theorems 81
4.1 The Law of Large Numbers . . . . . . . . . . . . . . . . . . . . . . 81
4.2 The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . 85
4.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
vi Contents
I Intermezzo 89
I.1 Uncountable Sample Spaces . . . . . . . . . . . . . . . . . . . . . . 89
I.2 An Event Without a Probability?! . . . . . . . . . . . . . . . . . . 90
I.3 Random Variables on Uncountable Sample Spaces . . . . . . . . . 92
5 Continuous Random Variables and Vectors 93
5.1 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2 Properties of Probability Measures . . . . . . . . . . . . . . . . . . 98
5.3 Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . 100
5.4 Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.5 Random Vectors and Independence . . . . . . . . . . . . . . . . . . 109
5.6 Functions of Random Variables and Vectors . . . . . . . . . . . . . 113
5.7 Sums of Random Variables . . . . . . . . . . . . . . . . . . . . . . 117
5.8 More About the Expectation; Variance . . . . . . . . . . . . . . . . 118
5.9 Random Variables Which are Neither Discrete Nor Continuous . . 122
5.10 Conditional Distributions and Expectations . . . . . . . . . . . . . 124
5.11 The Law of Large Numbers . . . . . . . . . . . . . . . . . . . . . . 131
5.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6 Infinitely Many Repetitions 137
6.1 Infinitely Many Coin Flips and Random Points in (0, 1] . . . . . . 138
6.2 A More General Approach to Infinitely Many Repetitions . . . . . 140
6.3 The Strong Law of Large Numbers . . . . . . . . . . . . . . . . . . 142
6.4 Random Walk Revisited . . . . . . . . . . . . . . . . . . . . . . . . 146
6.5 Branching Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7 The Poisson Process 153
7.1 Building a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.2 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.3 The Waiting Time Paradox . . . . . . . . . . . . . . . . . . . . . . 162
7.4 The Strong Law of Large Numbers . . . . . . . . . . . . . . . . . . 164
7.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
8 Limit Theorems 167
8.1 Weak Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.2 Characteristic Functions . . . . . . . . . . . . . . . . . . . . . . . . 169
8.3 Expansion of the Characteristic Function . . . . . . . . . . . . . . 173
8.4 The Law of Large Numbers . . . . . . . . . . . . . . . . . . . . . . 176
8.5 The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . 179
8.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
9 Extending the Probabilities 183
9.1 General Probability Measures . . . . . . . . . . . . . . . . . . . . . 183
Contents vii
A Interpreting Probabilities 187
B Further Reading 191
C Answers to Selected Exercises 193
Index 195
.
Edition Notes
The Physical Object
Edition Identifiers
Work Identifiers
Links outside Open Library
Community Reviews (0)
Lists
History
- Created April 8, 2025
- 2 revisions
Wikipedia citation
×CloseCopy and paste this code into your Wikipedia page. Need help?
| April 8, 2025 | Edited by meot | added the online edition (softcover, pdf) |
| April 8, 2025 | Created by meot | Added new book. |