Introductory Probability Theory
- Professors:
- Bassetti Federico, Dolera Emanuele
- Year:
- 2016/2017
- Course code:
- 504504
- ECTS:
- 9
- SSD:
- MAT/06
- DM:
- 270/04
- Lessons:
- 84
- Period:
- I semester
- Language:
- Italian
Objectives
The purpose of the course is to tell the beginning student of mathematics the basic facts of the theory of probability
Teaching methods
Lectures and exercises sessions
Examination
Written examination followed by an oral examination
Prerequisites
Mathematical analysis and linear algebra of the first year of the course in mathematics
Syllabus
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- Lévy version of the central limit theorem
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- Lévy version of the central limit theorem
Bibliography
Notes by E. Regazzini, available at http://www-dimat.unipv.it/~bassetti/
See also
Robert Ash (2008) Basic Pobability Theory, Dover
See also
Robert Ash (2008) Basic Pobability Theory, Dover
Modules
- Professor:
- Bassetti Federico
- Lessons:
- 56
- ECTS:
- 6
- Professor:
- Dolera Emanuele
- Lessons:
- 28
- ECTS:
- 3
Dipartimento di Matematica ''F. Casorati''
Università degli Studi di Pavia -
Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602