Elements of probability and statistics [electronic resource] : an introduction to probability with the De Finetti's approach and to Bayesian statistics / Francesca Biagini; Massimo Campanino.

1 Random numbers 2 Discrete distributions 3 One-dimensional absolutely continuous distributions 4 Multi-dimensional absolutely continuous distributions 5 Convergence of distributions 6 Discrete time Markov chains 7 Continuous time Markov chains 8 Statistics 9 Combinatorics 10 Discrete distributions 11 One-dimensional absolutely continuous distributions 12 Absolutely continuous and multivariate distributions 13 Markov chains 14 Statistics 15 Elements of combinatorics 16 Relations between discrete and absolutely continuous distributions 17 Some discrete distributions 18 Some one-dimensional absolutely continuous distributions 19 The normal distribution 20 Stirling's formula 21 Elements of analysis 22 Bidimensional integrals.

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.