- Docente: Maurizio Brizzi
- Credits: 8
- SSD: SECS-S/01
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Rimini
- Corso: First cycle degree programme (L) in Finance, Insurance and Business (cod. 8872)
Learning outcomes
At the end of the course, the candidate will be able to apply the
basic tools of probability, especially the most useful within
statistical analysis. Specifically, he will be able to calculate
the probability of complex events, to manage a wide range of
discrete and continuous random variables, and to know and apply the
main discrete random process patterns.
Course contents
Events and logical operations. Combinatorics. Axioms and elementary probability. Conditional probability and Bayes theorem. Discrete random variables and related models (Binomial, Geometric, Hypergeometric, Pascal, Poisson). Continuous random variables and related models (Uniform, Exponential, Gamma and Beta). Gaussian variables and derived distributions (Log-normal, Chi squared, Student t-distribution, Snedecor-Fisher F-distribution). Pareto Distribution. Bivariate discrete random variables. Covariance and its properties. Sequences and convergences of random variables. Bernoulli Theorem and Central Limit Theorem. Graduation function. Ordinal variables. Moment-generating function. Discrete Random Processes. Random walks. Poisson Processes with applications. Markov chains. Definition of martingale process and brownian motion.
Readings/Bibliography
Maurizio Brizzi. Calcolo delle probabilità con note introduttive di
inferenza statistica. Editrice Lo Scarabeo, Bologna, 2004
(only in Italian)
Maurizio Brizzi. Introduzione al calcolo delle probabilità e
all'inferenza statistica. Libreriauniversitaria.it, Limena (PD),
2014 (only in Italian)
Geoffrey Grimmett and David Stirzaker. Probability and Random
processes. Oxford University Press, 2001.
Teaching methods
Direct teaching and at least 4-6 hours of laboratory work.
Assessment methods
Written test with numerical applied exercises. Oral test concerning
theory and quick numerical examples.
Teaching tools
Working sheets containing theoretical features and exercises will be available to students (even in English).
Office hours
See the website of Maurizio Brizzi