First cycle (Basic training in science and technology)

This course deepens students’ understanding of probability theory, building on the fundamentals introduced in the first semester. It focuses on the rigorous study of random variables and their role in modeling uncertainty in engineering and scientific contexts.

Students explore both discrete and continuous random variables, including their probability distributions, cumulative distribution functions, and key properties. Standard probability laws are studied in detail, with emphasis on their practical use and interpretation.

A significant part of the course is devoted to the study of pairs of random variables, allowing students to analyze dependence structures through joint distributions, marginal distributions, and conditional probabilities. Concepts such as independence, expectation, covariance, and correlation are introduced to quantify relationships between variables.

The course also covers transformations of random variables and provides tools to handle more complex probabilistic models. Throughout the module, emphasis is placed on both theoretical rigor and practical application, preparing students for advanced topics in statistics, data analysis, and stochastic modeling.