- Docente: Alberto Lanconelli
- Crediti formativi: 6
- SSD: MAT/06
- Lingua di insegnamento: Inglese
- Modalità didattica: Convenzionale - Lezioni in presenza
- Campus: Bologna
- Corso: Laurea in Scienze statistiche (cod. 8873)
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dal 19/09/2022 al 25/10/2022
Conoscenze e abilità da conseguire
By the end of the course the student should know the basic theory of multidimensional random variables and sequences of random variables. In particular the student should be able: - to derive the distribution of transformed random variables - to derive joint, conditional and marginal probability density functions - to state the definition and recall the properties of multivariate normal distributions to investigate converge properties of sequences of random variables
Contenuti
- Useful inequalities and Lebesgue spaces
- Convergence concepts for sequences of random variables
- Borel-Cantelli lemma and applications
- Characteristic function of a random variable
- Weak and strong law of large numbers
- Central limit theorem
- Random vectors and multidimensional Gaussian distribution
Testi/Bibliografia
Lecture notes. Suggested readings:
- Kai Lai Chung, A course in Probability Theory - III edition, Aca-
demic Press, San Diego, 2001 - Rick Durrett, Probability: Theory and Examples - IV edition, Cam-
bridge University Press, Cambridge, 2013
Metodi didattici
Regular lectures and tutorials
Modalità di verifica e valutazione dell'apprendimento
One-hour written exam, articulated in a series of 3 exercises each with a maximum grade of 10 points, followed by an oral examination. Every exercise attains to elements of the syllabus covered during the course lectures. Online exams will be supported by the softwares Teams, Zoom and EOL (https://eol.unibo.it/)
Strumenti a supporto della didattica
Lecture notes and exercises with solutions
Orario di ricevimento
Consulta il sito web di Alberto Lanconelli
SDGs
L'insegnamento contribuisce al perseguimento degli Obiettivi di Sviluppo Sostenibile dell'Agenda 2030 dell'ONU.