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Elements of Probability and Statistics

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

  • Francesca Biagini
  • Massimo Campanino

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)

Table of contents

  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
      Pages 81-87
    8. Francesca Biagini, Massimo Campanino
      Pages 89-102
    9. Francesca Biagini, Massimo Campanino
      Pages 103-113
  3. Exercises

    1. Front Matter
      Pages 115-115
    2. Francesca Biagini, Massimo Campanino
      Pages 117-126
    3. Francesca Biagini, Massimo Campanino
      Pages 127-141
    4. Francesca Biagini, Massimo Campanino
      Pages 143-150
    5. Francesca Biagini, Massimo Campanino
      Pages 151-180
    6. Francesca Biagini, Massimo Campanino
      Pages 181-195
    7. Francesca Biagini, Massimo Campanino
      Pages 197-212
  4. Back Matter
    Pages 213-246

About this book

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