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 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.

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

Class lectures with exercises.

The exam consists of a written test and of an optional oral test.

The written exam consists in exercises, focused equitably on a part about probability theory and a part about statistics.
The presence of a theoretical question to verify the level of knowledge achieved by the student, is not excluded.

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.