Ateneo - UPO

Basic probability theory: the axioms of probability, Venn diagrams, space with equally likely outcomes, conditional probability, Bayes’ formula.
Random variables and expectation: discrete and continuous random variables, independent random variables, expected values, variance and covariance.
Special random variables: Bernoulli and binomial random 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, Bayesian estimators. Hypothesis testing and applications to computer science.

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 student 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.

Calculus and discrete mathematics. Elementary algebra and Linear Algebra.

Class lectures with exercises.

The exam consists of a written examination.

Written test. The exam consists in two exercises, one focused on probability and the other on statistics. Each exercise has 5 questions with increasing level of difficulty. Each exercise has also a theoretical question to value the preparation.

Basic probability theory: the axioms of probability, Venn diagrams, space with equally likely outcomes, conditional probability, Bayes’ formula.
Random variables and expectation: discrete and continuous random variables, independent random variables, expected values, variance and covariance.
Special random variables: Bernoulli and binomial random 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, Bayesian estimators. Maximal Likelihodd technique for common distributions. Confidence level and intervals. Hypothesis testing and applications to computer science.

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