Università degli Studi di Pavia

Dipartimento di Matematica ''F. Casorati''

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Introductory Probability Theory

Professors:
Regazzini Eugenio
Year:
2015/2016
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

Bibliography

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

THEORY


Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602