Ateneo - UPO

Basic probability theory: the axioms of probability, Venn diagrams, space with equally likely outcomes, conditional probability, Bayes formula.
Discrete and continuous random variables, independent random variables, expected values. Variance and covariance.
Special random variables: Bernoulli and binomial random variables, hypergeometric and geometric variables. Poisson distribution,
uniform random variables, normal random variables, exponential random variables. Central Limit Theorem. Basic statistics. Set of data,
mean, quartiles. Definition of sample statistics, sample variance. Parameter estimations. Hypothesis testing and applications.

Sheldon M. Ross: Introduction to probability and statistics for Engineers and scientists, Elsevier 2004 (Probabilità e Statistica per l'Ingegneria e le Scienze,Apogeo Education – Seconda Edizione 2008)

Introduce the students to the basic elements of theory and application of probability. Introduce the most important probability distributions with applications. Introduce the students to the basic elements of statistics, statistical mean, statistical variance, parameter estimations, hypothesis verifications.

Basic notions of the courses of Mathematical Analysis I and Discrete Mathematics.

Class lectures with exercises.

The exam consists of a written test composed of several exercises and one or more theoretical questions on the theoretical part. Students who pass the written part (with at least 18) can request an oral exam (optional). 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 the course to define the examination modalities, concerning academic aspects.

The written exam consists of 3-4 exercises concerning both the probability and statistics and of one or more questions on the theory part. The oral exam is optional and it is allowed only if a sufficient grade is achieved in the written test. The oral exam consists of questions concerning both probability and statistics and a discussion on the exercises contained in the written test.

Basic probability theory: the axioms of probability, Venn diagrams, space with equally likely outcomes, conditional probability, Bayes formula.
Discrete and continuous random variables, independent random variables, expected values. Variance and covariance.
Special random variables: Bernoulli and binomial random variables, hypergeometric and geometric variables. Poisson distribution,
uniform random variables, normal random variables, exponential random variables.
Central Limit Theorem. Basic statistics. Set of data, mean, quartiles. Definition of sample statistics, sample variance. Parameter estimations, Maximal Likelihodd technique for common distributions. Confidence level and intervals. Hypothesis testing and applications.

Knowledge of elementary probability theory. Knowledge of elementary statistics. Know how to apply probability and statistics theory to computer science and managing of data.