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## PROBABILITY

CODE 87081 2021/2022 8 cfu during the 2nd year of 8766 STATISTICA MATEM. E TRATTAM. INFORMATICO DEI DATI (L-35) - GENOVA 8 cfu during the 3nd year of 8760 MATEMATICA (L-35) - GENOVA MAT/06 GENOVA 1° Semester Prerequisites (for future units) This unit is a prerequisite for: Mathematical Statistics and Data Management 8766 (coorte 2019/2020) MATHEMATICAL STATISTICS 52503 STOCHASTIC PROCESSES 57320 Mathematical Statistics and Data Management 8766 (coorte 2020/2021) MATHEMATICAL STATISTICS 52503 STOCHASTIC PROCESSES 57320 AULAWEB

## 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.

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

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

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

### Exam schedule

Date Time Location Type Notes
19/01/2022 09:30 GENOVA Scritto
14/02/2022 09:30 GENOVA Scritto
08/06/2022 09:30 GENOVA Scritto
11/07/2022 09:30 GENOVA Scritto
09/09/2022 09:30 GENOVA Scritto