DAES04A - CALCOLO DELLE PROBABILITA'

The course aims to achieve the overall objective of the study program, which is to train professional figures skilled in data management and analysis in all work contexts.
The course aims to provide students with the basic concepts of probability theory, such as events, sample spaces, conditional probability, Bayes' theorem, and probability distributions. It also aims to introduce the main discrete and continuous random variables, their distributions, and explain how to calculate and interpret parameters like mean, variance, and moments. The study of key probability theorems, such as the law of large numbers, the central limit theorem, and limit distributions, is also included. Finally, some probabilistic models are presented, aimed at describing random phenomena and analyzing real-world situations through probability.
By the end of the course, students will have gained both theoretical and practical knowledge of probability theory and key random variables. This knowledge, which is applicable across various economic, managerial, and social fields, will enable students to model real-world phenomena and conduct investigations, experiments, and data analysis.
To this end, the course aims to impart the following skills and knowledge:
KNOWLEDGE AND UNDERSTANDING CAPACITY
- basic concepts of probability theory;
- main probabilistic models (discrete and continuous) such as the binomial, Poisson, and normal random variables;
- expected value, variance, and, in general, moments of random variables;
- key probability theorems.
To achieve this, the course aims to convey the following specific skills and knowledge:
KNOWLEDGE AND UNDERSTANDING CAPACITY (applied)
- use mathematical tools to solve problems of a probabilistic and statistical nature;
- apply probability theorems and axioms, and use the main random variables;
- use statistical software to conduct data analysis and produce summary reports.
JUDGMENT AUTONOMY:
- independently identify the tools and probabilistic models to use in formalizing and analyzing a real-world phenomenon;
- present oral analytical and synthetic considerations on the fundamental aspects of the discipline;
- provide a critical assessment of the results of analyses and draw conclusions, including through interdisciplinary connections, that offer strategic insights and their socio-economic implications.
COMMUNICATION SKILLS:
- use statistical language pertinently;
- communicate the results of statistical analyses and the underlying logical reasoning, both in writing and orally, even in interdisciplinary contexts and in the presence of non-expert audiences.
LEARNING SKILLS:
- conduct individual and group research on specific aspects and topics of interest in various economic and social application domains.