The purpose of the course is to tell the beginning student of mathematics the basic facts of the theory of probability

Lectures and exercises sessions

Written examination followed by an oral examination

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

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

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

THEORY