- Docente: Pietro Rigo
- Credits: 6
- SSD: MAT/06
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Statistical Sciences (cod. 9222)
Learning outcomes
By the end of the course the student acquires the fundamental notions of the theories of conditional probability and weak convergence of probability measures. In particular, the student is able to investigate the asymptotic behaviour of sequences of probability measures arising in statistical inference and to coherently employ the concept of conditional probability in the statistical investigation.
Course contents
Probability spaces
A few elementary notions of measure theory
Random variables and their probability distributions
Probability measures on R and R^n
Moments
Conditional distributions
Characteristic functions
Weak convergence of probability measures
Other modes of convergence
Laws of large numbers
Central limit theoremsReadings/Bibliography
Billingsley P. (1986) Probability and measure, Wiley, New York
Dall'Aglio G. (1987) Calcolo delle probabilita', Zanichelli.
Grimmett G. and Stirzaker D. (2001) Probability and random processes, Oxford University Press.
Teaching methods
Lectures 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 quoted above
Office hours
See the website of Pietro Rigo