Ateneo - UPO

Introduction to the theory of probability and statistical inference

Sheldon M. Ross: Probabilità e Statistica per l'Ingegneria e le Scienze, Apogeo Education - Seconda Edizione 2008

Introduce the student to the theory and applications of probability with emphasis on the most important probability distributions. Introduce the student to the basic elements of statistics with emphasis on parameter estimation and hypothesis testing

Differential and integral calculus in one dimension and more if possible

Class lectures with exercises

The exam consists of a written examination.
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/services-students-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 tre course to define the examination modalities, concerning academic aspects

The written exam consists in two exercises, one focused on probability and the other on statistics. Each exercise has also a theoretical question to value the knowledge of the theory

- Basic probability theory: fundamental axioms, space with equally likely outcomes and combinatorics, conditional probability, Bayes' formula

- Random variables: discrete and continuous variables, most relevant variables (Bernoulli and binomial variables, Poisson variables, uniform, normal, and exponential random variables), independent variables, expected value

- Limit theorems: law of large numbers, central limit theorem

- Descriptive statistics: set of data, sample mean and median, sample variance

- Basic inferential statistics: mean and variance estimators, maximum likelihood estimators, confidence level and intervals, hypothesis testing

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