- 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)
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
- Characteristic function of a random variable
- Random vectors and multidimensional Gaussian distribution
- Convergence concepts for sequences of random variables
- Borel-Cantelli lemma and applications
- Weak and strong law of large numbers
- Convergence in distribution, central limit theorem and applications
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
Modalità di verifica e valutazione dell'apprendimento
Written and oral exams
Strumenti a supporto della didattica
Notes provided at the beginning of the course. Exercises with solutions.
Orario di ricevimento
Consulta il sito web di Alberto Lanconelli