2021/2022

2022/2023

DM270

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

MATHEMATICS

PERCORSO COMUNE

2°

1st semester (29/09/2022 - 13/01/2023)

9

84 lesson hours

Italian

WRITTEN AND ORAL TEST

DOLERA EMANUELE (titolare) - 3 ECTS
ORRIERI CARLO - 6 ECTS

Mathematical analysis and linear algebra of the first year of the course in mathematics

The purpose of the course is to introduce the students to the basic facts of the theory of probability.

Extended summary

1.- Definition of probability.
2.- Probability distribution of a random number
3.- Conditional probabilities and stochastic independence
4.- Distribution of a random vector and conditional distributions in some special cases
5.- Numerical characteristics of a probability distribution: expectation, variance, moments, regression, covariance, correlation
6.- Integral transformations: characteristic function, moment generating function and their application to the calculus of distinguished probability distributions, which are of interest for statistics
7.- Some remarkable inequalities and hints of limit theorems in probability theory: elementary examples of weak laws of large numbers and Lindeberg- Levy version of the central limit theorem

Theorical lectures (56h) and exercises sessions (28h). During exercises sessions the teacher will solve exercises on the arguments develpoed during the lectures.

Notes by E. Regazzini, available at http://www-dimat.unipv.it/~bassetti/
See also
Robert Ash (2008) Basic Pobability Theory, Dover

Written examination followed by an oral examination.
The written examination is a set of 4 problems on the specific topics treated during the course. If the student obtains a grade of 18/30, he/she must sustain an oral examination. During the oral examination the student will be required to state some definitions, theorems with proofs or to solve some exercise on the topic trated during the course. The final grade is established by the commission.