Further Topics in Probability and Statistics

Credits

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/06 Probability and Mathematical Statistics.

Examination method

Oral exam.

Learning
objectives

The course aims to complete students’ education and knowledge in this specific disciplinary field, with an approach that will emphasise aspects and methods useful for teaching.
To this end, each topic will be accompanied by examples on real data analysed using the R language (or a spreadsheet), and (at least) one statistical survey will be carried out in the laboratory.

Syllabus

Paradoxes and problems representing conceptual knots in the teaching of probability. Random number generation and the Monte Carlo method. Univariate and bivariate descriptive statistical analysis. Statistical hypothesis testing. Simple and multivariate regression. Models for time series analysis. Data representation (histogram, cumulative histogram and the Glivenko-Cantelli theorem). Statistical inference.

Expected learning
outcomes

At the end of the course, students must demonstrate that they

know the content presented, up to the level of proving the results, and understand its potential for applications and its usefulness for preparing meaningful teaching units;
are able to apply the knowledge acquired to carry out statistical surveys in order to obtain the appropriate quantitative and qualitative answers for the data available;
are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
are able to identify the most appropriate methods to analyse and solve a problem related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Command of the subject matter, clarity of exposition, rigour in the use of language, confidence in using the notions acquired.

Further Topics in Probability and Statistics