- Docente: Simone Giannerini
- 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
- Fundamentals of probability
- Random variables
- Moment generating functions
- Trasforming and simulating random variables
- Bivariate distributions
- Random Vectors
- Functions of a random vectors
- Convergence of sequences of random variables and limit theorems
Readings/Bibliography
1. Multivariate probability, J.H. McColl, 2004, Arnold publisher, London.
- Chapter 1: all of it;
- Chapter 2: all of it;
- Chapter 3: all of it;
- Chapter 4: all of it;
- Chapter 5: 5.1, 5.2, 5.4;
- Chapter 6: all of it;
- Chapter 7: 7.1, 7.2;
2. Corso di Probabilità, O. Lessi, 1993, Metria, Padova.
- Chapter 6: all of it, except 6.6;
- Chapter 7: up to 7.2.1 (not included); 7.3, 7.4.
Teaching methods
- Lessons
- Classes with guided exercises
Assessment methods
A 2-hour written examination that includes
- Exercises similar to those seen in classes (see the online material);
- Questions on topics covered during the lessons including the proofs of the most important theorems;
Teaching tools
Visit my web page for the direct link to the teaching material
http://www2.stat.unibo.it/giannerini/
Links to further information
http://www2.stat.unibo.it/giannerini/
Office hours
See the website of Simone Giannerini