CODE 87081 ACADEMIC YEAR 2024/2025 CREDITS 8 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA 8 cfu anno 2 STATISTICA MATEM. E TRATTAM. INFORMATICO DEI DATI 8766 (L-35) - GENOVA 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 VERONICA UMANITA' Ricevimento: By appointment by email. ERNESTO DE VITO Ricevimento: Send a message to ernesto.devito@unige.it 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. Agenda 2030 - Sustainable Development Goals Quality education Gender equality