OVERVIEW

This course is dedidcet to introduce basic concepts in Probability Theory. the aim is to give a solid background and the instrumentes to understand the probabilistic language: the student shound be able to build and analyse easy stochastic models. The links with other disciplines as Analysis and Statistics will be presented.

AIMS AND CONTENT

LEARNING OUTCOMES

Introduction to modeling of random phenomena.

SYLLABUS/CONTENT

Introduction of probability: assiomatic costruction of probabiloty spaces. Concept of independence, conditional probability. Bayes Theorem. Random variables: distribution function, expectation, variance (Bernoulli, Binomiale, Geometrica, Binomiale Negativa, Ipergeometrica, Normale, Uniforme, Cauchy, Esponenziale, Gamma, Chi-Quadro, t di Student,...). Markov and Chebychev inequalities. Random vectors. Characteristic functions. Convergence definitions and theorems. Law of large numbers and Central limit theorem. Stochastic simulation.

RECOMMENDED READING/BIBLIOGRAPHY

K. L. Chung, A Course in probability Theory

J. Jacod, P. Protter, Probability Essentials

TEACHERS AND EXAM BOARD

Exam Board

EMANUELA SASSO (President)

ERNESTO DE VITO

VERONICA UMANITA' (President Substitute)

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of a written test and an oral exam.

Exam schedule