# Elements of Probability and Statistics

## An Introduction to Probability with de Finetti’s Approach and to Bayesian Statistics

• Francesca Biagini
• Massimo Campanino
Textbook

Part of the UNITEXT book series (UNITEXT, volume 98)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT, volume 98)

1. Front Matter
Pages i-xv
2. ### Probability

1. Front Matter
Pages 1-1
2. Francesca Biagini, Massimo Campanino
Pages 3-26
3. Francesca Biagini, Massimo Campanino
Pages 27-42
4. Francesca Biagini, Massimo Campanino
Pages 43-56
5. Francesca Biagini, Massimo Campanino
Pages 57-72
6. Francesca Biagini, Massimo Campanino
Pages 73-80
7. Francesca Biagini, Massimo Campanino
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8. Francesca Biagini, Massimo Campanino
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9. Francesca Biagini, Massimo Campanino
Pages 103-113
3. ### Exercises

1. Front Matter
Pages 115-115
2. Francesca Biagini, Massimo Campanino
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3. Francesca Biagini, Massimo Campanino
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4. Francesca Biagini, Massimo Campanino
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5. Francesca Biagini, Massimo Campanino
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6. Francesca Biagini, Massimo Campanino
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7. Francesca Biagini, Massimo Campanino
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4. Back Matter
Pages 213-246

### Introduction

This book provides an introduction to elementary probability and to Bayesian statistics using de Finetti's subjectivist approach. One of the features of this approach is that it does not require the introduction of sample space – a non-intrinsic concept that makes the treatment of elementary probability unnecessarily complicate – but introduces as fundamental the concept of random numbers directly related to their interpretation in applications. Events become a particular case of random numbers and probability a particular case of expectation when it is applied to events. The subjective evaluation of expectation and of conditional expectation is based on an economic choice of an acceptable bet or penalty. The properties of expectation and conditional expectation are derived by applying a coherence criterion that the evaluation has to follow. The book is suitable for all introductory courses in probability and statistics for students in Mathematics, Informatics, Engineering, and Physics.

### Keywords

Bayesian statistics Conditional expectation Logical dependence Markov chains Probability

#### Authors and affiliations

• Francesca Biagini
• 1
• Massimo Campanino
• 2
1. 1.Dept. of MathematicsLudwig-Maximilians UniversitätMunichGermany
2. 2.Dept. of MathematicsUniversità di BolognaBolognaItaly

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-07254-8
• Copyright Information Springer International Publishing Switzerland 2016
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics
• Print ISBN 978-3-319-07253-1
• Online ISBN 978-3-319-07254-8
• Series Print ISSN 2038-5714
• Buy this book on publisher's site
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