- Docente: Alberto Lanconelli
- Credits: 6
- SSD: MAT/06
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Statistical Sciences (cod. 8873)
Learning outcomes
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
Course contents
- 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
Readings/Bibliography
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
Teaching methods
Regular lectures
Assessment methods
Written and oral exams
Teaching tools
Notes provided at the beginning of the course. Exercises with solutions.
Office hours
See the website of Alberto Lanconelli