PROBABILITY - NOTIONS
Stampa
Enrollment year
2019/2020
Academic year
2020/2021
Regulations
DM270
Academic discipline
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Course
MATHEMATICS
Curriculum
PERCORSO COMUNE
Year of study
Period
1st semester (01/10/2020 - 20/01/2021)
ECTS
9
Lesson hours
84 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
DOLERA EMANUELE (titolare) - 6 ECTS
ORRIERI CARLO - 3 ECTS
Prerequisites
Mathematical analysis and linear algebra of the first year of the course in mathematics
Learning outcomes
The purpose of the course is to introduce the students to the basic facts of the theory of probability.
Course contents
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
Teaching methods
Theorical lectures (56h) and exercises sessions (28h). During exercises sessions the teacher will solve exercises on the arguments develpoed during the lectures.
Reccomended or required readings
Notes by E. Regazzini, available at http://www-dimat.unipv.it/~bassetti/
See also
Robert Ash (2008) Basic Pobability Theory, Dover
Assessment methods
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.
Further information
Sustainable development goals - Agenda 2030