Elements of Probability and Statistics: An Introduction to Probability with de Finetti’s Approach and to Bayesian Statistics (UNITEXT)

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.