Salta al contenuto principale della pagina

PROBABILITY

CODE 87081
ACADEMIC YEAR 2022/2023
CREDITS
  • 8 cfu during the 3nd year of 8760 MATEMATICA (L-35) - GENOVA
  • 8 cfu during the 2nd year of 8766 STATISTICA MATEM. E TRATTAM. INFORMATICO DEI DATI (L-35) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/06
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 1° Semester
    PREREQUISITES
    Prerequisites (for future units)
    This unit is a prerequisite for:
    • Mathematical Statistics and Data Management 8766 (coorte 2021/2022)
    • MATHEMATICAL STATISTICS 52503
    • STOCHASTIC PROCESSES 57320
    • Mathematical Statistics and Data Management 8766 (coorte 2020/2021)
    • MATHEMATICAL STATISTICS 52503
    • 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.

    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

    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
    19/01/2023 09:30 GENOVA Scritto
    10/02/2023 09:30 GENOVA Scritto
    07/06/2023 09:30 GENOVA Scritto
    10/07/2023 09:30 GENOVA Scritto
    08/09/2023 09:30 GENOVA Scritto