Ateneo - UPO

Introduction to the theory of probability and statistical inference

- Lecture notes uploaded on the IT platform DIR - Paolo Baldi: calcolo delle probabilità e statistica, McGraw-Hill 1998 - Sheldon M. Ross: Probabilità e Statistica per l'Ingegneria e le Scienze, Apogeo Education - Seconda Edizione 2008

Introducing the student to the theory and applications of probability with emphasis on discrete random variables. Introducing the student to the basic elements of statistics with emphasis on parameter estimation

Differential and integral calculus in one dimension and more

Class lectures with exercises

Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the __Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/servicesstudents-physical-or-learning-disabilities. Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities

The exam consists of a written and an oral examination. The written test includes two exercises (one on probability and one on statistics), which are then corrected and discussed in the oral test. The oral test also includes some theoretical questions. In order to pass students must be able to sketch out both exercises

- Basic probability theory: fundamental axioms, space with equally likely outcomes and combinatorics, conditional probability, Bayes' formula, repeated trials - Random variables and expectation: random variables on finite spaces, independent variables, expected value, variance and covariance, binomial random variables - Limit theorems: Markov and Chebyshev inequalities, law of large numbers, central limit theorem - Basic inferential statistics: sample statistics, maximum likelihood estimators - Shannon entropy: entropy as a measure of uncertainty, exponential families and estimation of their parameters - Gaussian random variables: introduction to infinite probability spaces, Gaussian sample, confidence intervals for the mean and the variance

Knowledge of elementary probability theory and statistics. Ability to propose simple models for data description and to infer their parameters