Università Roma Tre

The student will be introduced to the elements of probability calculus and the theory of random variables, through the notions of space of events and the axioms of probability. He will be introduced to the concept of conditional probability and its possible applications. The case of discrete and continuous random variables, scalar and vector, will be treated through the introduction of the concepts of probability distribution, mean value, variance, moments with integer exponent, correlation and covariance. The fundamental theorems of the theory of random numerical variables will be studied with a focus on the law of large numbers and the central limit theorem.
We will then move on to the introduction of the fundamental concepts of sample space statistics through the theory of statistical estimators and confidence intervals. The concept of statistical hypothesis tests will then be introduced, exposing the main cases and their field of applicability. Finally, some elements of descriptive statistics and the linear regression technique will be introduced.

1) Calcolo delle probabilità e statistica per le scienze e l'ingegneria, Pasquale Erto, McGraw-Hill (2008)
2) Probabilità e statistica per l'ingegneria e le scienze, Sheldon M. Ross, Maggioli editore (2023)