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## PROBABILITY

CODE 87081 2018/2019 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 MAT/06 GENOVA (Mathematical Statistics and Data Management) 1° Semester Prerequisites (for future units) This unit is a prerequisite for: Mathematical Statistics and Data Management 8766 (coorte 2016/2017) MATHEMATICAL STATISTICS 52503 STOCHASTIC PROCESSES 57320 Mathematical Statistics and Data Management 8766 (coorte 2017/2018) MATHEMATICAL STATISTICS 52503 STOCHASTIC PROCESSES 57320 AULAWEB

## 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

VERONICA UMANITA' (President)

EMANUELA SASSO (President)

ERNESTO DE VITO

## 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
15/01/2019 09:30 GENOVA Scritto
05/02/2019 09:30 GENOVA Scritto
25/06/2019 09:30 GENOVA Scritto
16/07/2019 09:30 GENOVA Scritto
03/09/2019 09:30 GENOVA Scritto