- Docente: Maurizio Brizzi
- Credits: 8
- SSD: STAT-01/A
- Language: Italian
- Teaching Mode: In-person learning (entirely or partially)
- Campus: Rimini
- Corso: First cycle degree programme (L) in Statistics, Finance and Insurance (cod. 6660)
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
Random trials, events and logical operations. Combinatorics. Axioms and elementary probability. Conditional probability, independence 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 and continuous Random Processes. Random walks. Poisson Processes with applications. Markov chains and classification of states. 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 including three exercises with numerical applications. Each exercise can be valued between 9 and 12 points. Usually the first exercise is related to elementary probability, the second involves random variables, the third concerns stochastic processes. Oral test is dedicated to the complete course theory, jointly with some quick numerical examples.
- Evaluation scale:
30 e lode (A+) = excellent
29 - 30 (A) = very good
27 - 28 (B+) = good
25 - 26 (B) = fairly good
22 - 24 (C) = more than sufficient
20 - 21 (D) = sufficient
18 - 19 (E) = barely sufficient
- Students with specific learning disorders (SLD) or temporary or permanent disabilities are encouraged to contact the University's dedicated support office in good time
https://site.unibo.it/studenti-con-disabilita-e-dsa/en
The office will propose any appropriate accommodations for eligible students. These accommodations must be submitted to the course instructor for approval at least 15 days in advance. The instructor will assess their appropriateness, taking into account the intended learning outcomes of the course.
- The use of AI tools during the exam session is prohibited in all ways. Any use of AI tools constitutes a breach of academic integrity.
Teaching tools
Working sheets in Power Point are available to students, covering all the Course topics and containing theoretical features, examples and exercises (even in English, if requested).
Links to further information
https://www.unibo.it/sitoweb/maurizio.brizzi/
Office hours
See the website of Maurizio Brizzi