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CODE 87081
ACADEMIC YEAR 2024/2025
CREDITS
SCIENTIFIC DISCIPLINARY SECTOR MAT/06
LANGUAGE Italian
TEACHING LOCATION
  • GENOVA
SEMESTER 1° Semester
PREREQUISITES
Propedeuticità in uscita
Questo insegnamento è propedeutico per gli insegnamenti:
  • Mathematical Statistics and Data Management 8766 (coorte 2022/2023)
  • MATHEMATICAL STATISTICS 52503
  • Mathematical Statistics and Data Management 8766 (coorte 2022/2023)
  • STOCHASTIC PROCESSES 57320
  • Mathematical Statistics and Data Management 8766 (coorte 2023/2024)
  • MATHEMATICAL STATISTICS 52503
  • Mathematical Statistics and Data Management 8766 (coorte 2023/2024)
  • STOCHASTIC PROCESSES 57320
TEACHING MATERIALS 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.

AIMS AND LEARNING OUTCOMES

The expected learning outcomes stipulate that the student should be able to handle the basic definitions of probability spaces , the elementary rules of computation, the concept of conditioning and independence, that he/she has acquired the notion of random variable and random vector, of the distribution and possible joint and marginal density with knowledge of the role of their main characteristics (mean, variance, moments, generating functions). The student should be able to construct simple probabilistic models (possibly adapting classical schemes) in the discrete and continuous and to discuss the results given by the models.

PREREQUISITES

For this teaching, it may be useful to know how to handle basic tools of analysis, especially integral calculus and numerical series. In addition, explicit references to the basic tools of descriptive statistics will be made throughout the course.

TEACHING METHODS

Teaching involves theory (four hours per week) and exercise classes (three hours per week) coordinated with each other. Approximately two or more guided (ungraded) exercises are planned to enable the student to monitor his or her preparation in progress. Exercise sheets will be uploaded to aulaweb upon completion of each topic covered.

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

  • P. Baldi, Calcolo delle Probabilità
  • K. L. Chung, A Course in probability Theory
  • J. Jacod, P. Protter, Probability Essentials

TEACHERS AND EXAM BOARD

Exam Board

ERNESTO DE VITO (President)

VERONICA UMANITA'

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.

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.

ASSESSMENT METHODS

In the written test, the student is asked to solve exercises covering the entire syllabus. The duration of the test is three hours. Students are not allowed to consult books or notes, but are advised to prepare a ‘formulary’ with the formulas and results useful for the test. To participate in the written test, it is necessary to register on the UNIGE website. The written test is considered sufficient if it obtains a mark of 18/30 or higher. Only in very exceptional cases does the exam board reserve the right to lower this threshold. There are no intermediate tests that replace the written test.

The oral test is designed to verify the absence of substantial gaps in the student's preparation and is therefore conducted on the basis of the deficiencies highlighted by the written test. It may be taken in the roll call of the written test or in subsequent roll calls (by the end of the current academic year). In the oral examination, the student is required to be able to introduce and describe the main concepts seen in the lecture, with particular emphasis on the statement and demonstration of the main theorems. In order to understand whether the student is able to use the tools of the calculus of probability, exercises will also be proposed. If the oral examination proves insufficient, highlighting fundamental deficiencies in the student's preparation, the committee reserves the right to cancel the written examination as well. 

The written and oral examination will focus mainly on the topics covered during the lectures and will aim to assess not only whether the student has achieved an adequate level of knowledge, but whether he/she has acquired the ability to critically analyse probability-related problems.

Exam schedule

Data appello Orario Luogo Degree type Note
14/01/2025 09:30 GENOVA Scritto
10/02/2025 09:30 GENOVA Scritto
04/06/2025 09:30 GENOVA Scritto
07/07/2025 09:30 GENOVA Scritto
05/09/2025 09:30 GENOVA Scritto

FURTHER INFORMATION

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.
 

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