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.
Introduction to modeling of random phenomena.
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.
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 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.
Ricevimento: By appointment by email.
Ricevimento: Send a message to ernesto.devito@unige.it
ERNESTO DE VITO (President)
VERONICA UMANITA'
The class will start according to the academic calendar.
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.
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.
