Elements of Probability and Statistics: An Introduction to Probability with de Finetti’s Approach and to Bayesian Statistics (UNITEXT Book 98)

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. Front Matter....Pages i-xv Front Matter....Pages 1-1 Random Numbers....Pages 3-26 Discrete Distributions....Pages 27-42 One-Dimensional Absolutely Continuous Distributions....Pages 43-56 Multi-dimensional Absolutely Continuous Distributions....Pages 57-72 Convergence of Distributions....Pages 73-80 Discrete Time Markov Chains....Pages 81-87 Continuous Time Markov Chains....Pages 89-102 Statistics....Pages 103-113 Front Matter....Pages 115-115 Combinatorics....Pages 117-126 Discrete Distributions....Pages 127-141 One-Dimensional Absolutely Continuous Distributions....Pages 143-150 Absolutely Continuous and Multivariate Distributions....Pages 151-180 Markov Chains....Pages 181-195 Statistics....Pages 197-212 Back Matter....Pages 213-246