Elements of Probability and Statistics An introduction to probability with the De Finetti approach and to Bayesian statistics

This book provides an introduction to elementary probability and to Bayesian mathematical statistics using de Finetti's subjectivistic 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 usual treatment of elementary probability unnecessarily heavy - but it introduces as fundamental the concept of random numbers directly related to its 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 a coherence criterium that the evaluation has to follow. The book is suitable for all introductory courses in probability and statistics for students in Mathematics, Informatics, Engineering, Physics.