il portale dello studente

(portale studente principale)

(gestione avvisi)

(materiale didattico)

Istruzioni per accesso

studenti

laureandi

docenti

personale di gestione

I corsi

Guide dello studente

Orario delle lezioni

Calendario degli appelli

Ricevimenti dei docenti

Le persone

Guide dello studente

Orario delle lezioni

Calendario degli appelli

Ricevimenti dei docenti

Le persone

Statistics

Aim of the course

Students will acquire the elements of statistical theory and practice necessary for analysing and interpreting data sets, and extracting from them information to support decision-making in conditions of uncertainty, typical of socio-economic-business and financial situations. The two fundamental steps of descriptive and inferential statistical analysis will be covered, exemplified through probability calculations, numerical processing and simulations using professional statistical software packages, as well as by tutorial exercises and a portion of examination conducted in the computer lab. Students will gain and understanding of how, and to what extent, the results obtained from a statistical sample can be extrapolated to its parent statistical population, with references to applications in manufacturing (e.g. statistical quality control) and opinion surveys (e.g. in business marketing).

Syllabus

Relative frequency and frequency density, statistical indicators and graphical representations. Relative frequency of a random event as an indicator of the likelihood of its occurrence. Introduction to probability calculation and to one-dimensional probabilistic models (random variables) generating the observed data, and their simulation via software. In particular: the Gaussian and lognormal models (e.g. for the distribution of the random fluctuations in listed share prices and yields). Two-dimensional and n-dimensional models (random vectors) and their software simulation. Random vector functions, two-dimensional dependence analysis, tabular and graphical representations, linear correlation. Exact and asymptotically approximated distributions (central limit theorem) of the sum and of the "sum divided by n" (sampling average), particularly in the Gaussian and Bernouilli case. Introduction to inferential statistics: census and sampling. Statistical population, random sample and taking of the sample, sampling function, estimators of a population parameter and their properties. Point and interval estimation of the expected value, point estimation of the variance. Parametric statistical tests (e.g. in statistical quality control): statistical hypothesis, type I and type II errors and their probability, rejection and acceptance ranges for the expected value in the various cases of simple and compound hypotheses. Linear regression model: least squares method, estimation of coefficients and statistical tests.

Examinations

Students can choose between the following two methods of assessment. Method (1): Intermediate tests (written, and with use of statistical software) during the course and at the end, covering the portions of the syllabus studied up until that point; the final result will be an average of the grades obtained in the intermediate tests. Method (2): students who do not pass, or choose not to sit, the two intermediate tests will be evaluated by a single test covering the entire course syllabus, to be taken during the sessions scheduled in the academic calendar.

Reading list

Spiegel, M. R., et al., *Probabilità e statistica*, Milano, Editore McGraw-Hill, Milano,2000.

Piccarreta, Veronese, *Lezioni di inferenza statistica*, Editore Shonenfeld & Ziegler, Milano, 2002.

Additional study materials and references may be given during the course.