# PROBABILITY

iten
Code
87081
2020/2021
CREDITS
8 credits during the 2nd year of 8766 Mathematical Statistics and Data Management (L-35) GENOVA

8 credits during the 3nd year of 8760 Mathematics (L-35) GENOVA

SCIENTIFIC DISCIPLINARY SECTOR
MAT/06
TEACHING LOCATION
GENOVA (Mathematical Statistics and Data Management)
semester
1° Semester
Prerequisites
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 2018/2019)
• MATHEMATICAL STATISTICS 52503
• STOCHASTIC PROCESSES 57320
Teaching materials

## 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

Office hours: Thursday: 14.00-15.30, office 836,&nbsp;&nbsp;or by arrangement made by email.

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
19/01/2021 09:30 GENOVA Scritto
15/02/2021 09:30 GENOVA Scritto
09/06/2021 09:30 GENOVA Scritto
12/07/2021 09:30 GENOVA Scritto
01/09/2021 09:30 GENOVA Scritto