The general objective of the course is to provide students with a formal introduction to probability theory, which underlies disciplines such as statistics and the study of stochastic processes. The second educational objective is more applied and refers to the understanding of the context in which probabilistic concepts and random variables are required to be introduced, and based on this understanding, students are required to know how to use the most appropriate probabilistic tool and the best random variable to describe the context and phenomenon of interest.

Specifically, the course aims to:
1) provide an understanding of how random phenomena can be modeled from a mathematical point of view through the concepts of probability space and random variable;
2) define the main characteristics of random variables such as law, discrete and continuous density function, moments;
3) introduce the main probability distributions both discrete and continuous;
4) introduce the most important results on convergence of random variables, such as the law of large numbers and the central limit theorem, and make students understand their importance in solving theoretical and applied problems.

Upon completion of the course, students are expected to:
1) to be able to formalize probability calculus problems in both theoretical and applied contexts;
2) have acquired the methodologies necessary to compute probabilities, expected values, variance, expected values of functions of random variables and moment generating functions;
3) know the remarkable cases of discrete and continuous random variables and know in what contexts to apply them;
4) are able to apply results on convergence of random variables to the solution of theoretical and practical problems.