- Docente: Pietro Rigo
- Credits: 6
- SSD: MAT/06
- Language: Italian
- 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 be able to use the basic (elementary) tools of probability theory, having statistical applications in mind. Specifically, the student should be able to calculate the probability of (possibly complex) events, employing the basic results of probability theory, as well as simple mathematical models involving discrete and/or absolutely continuous random variables.
Course contents
Probability spaces and their elementary properties
Various definitions of probability (just a brief mention)
Random variables and their probability distributions
Independence
Probability measures on R and R^n (including distribution functions and the classification of laws as discrete, singular continuous and absolutely continuous)
List of the main probability laws on R and multivariate Gaussian law
Transformation of variables
Moments
Conditional distributions
Characteristic functions (just a brief mention)
Convergence of random variables
Laws of large numbers
Central limit theorems
Readings/Bibliography
In order to prepare the exam, the notes (taken by the student directly) are enough, obviously provided they are correct and complete. If notes are not sufficiently clear, and/or to deepen the various topics, the following text-books are suggested:
Dall'Aglio G. (1987) Calcolo delle probabilita', Zanichelli.
Grimmett G. and Stirzaker D. (2001) Probability and random processes, Oxford University Press.
Teaching methods
Lessons and class exercises.
Assessment methods
The first part of the exam consists of a written assignment. The second part, subject to overcoming the first, lies in an oral interview
Teaching tools
Notes and the text-books mentioned above.
Office hours
See the website of Pietro Rigo