Elements of Probability and Statistics: An Introduction to Probability with de Finetti's Approach and to Bayesian Statistics

Provides an introduction to elementary probability and to Bayesian statistics using de Finetti's subjectivist approach Introduces as fundamental the concept of random numbers Includes numerous exercises covering most topics treated in the theoretical part of the book 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. Topics Probability Theory and Stochastic Processes Statistical Theory and Methods Probability and Statistics in Computer Science Business Mathematics Mathematical Methods in Physics Appl. Mathematics / Computational Methods of Engineering