Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2020/2021
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3° Year activated in the A.Y. 2021/2022
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Probability and Statistics (2020/2021)
Teaching code
4S02843
Credits
9
Coordinator
Language
Italian
Also offered in courses:
- Probability of the course Bachelor's degree in Applied Mathematics
The teaching is organized as follows:
Learning outcomes
The course introduces basic concepts of Probability Theory, with particular emphasis on its formal description starting from its axiomatization due to A. Kolmogorov. The emphasis will be placed on the formal derivation of the modern Probability Theory starting from the axiomatization of A.N. Kolmogorov. The course aims to provide rigorous probabilistic training which allows the student to master the techniques mathematics at the base of the modern theory of probabilities, and their application in computational-modeling and economic-financial fields. With the same spirit based on mathematical rigor, elements of Descriptive Statistics and Analysis of historical series will also be introduced.
Program
The entire course will be available online. In addition, a number of the lessons/all the lessons (see the course
schedule) will be held in-class.
Discrete probability spaces. Elements of combinatorial calculus. Conditional probability and independence.
Applications: random permutations, percolation.
Discrete random variables and distributions. Independence of random variables. Expectation and inequalities. Notable classes of discrete random variables.
Applications: the law of small numbers, the binomial model in finance, the collector's problem.
Probability spaces and general random variables.
Absolutely continuous random variables. Notable classes of absolutely continuous random variables. Absolutely continuous random vectors. The Poisson process. Normal laws.
The law of large numbers. The central limit theorem and normal approximation.
Elements of stochastic simulation.
Basic notions of inferential statistics: unbiased and efficient estimators. Normal samples. Maximum likelihood estimators.
Textbook: F. Caravenna, P. Dai Pra, Probabilità. Un'introduzione attraverso modelli e applicazioni - UNITEXT - La matematica per il 3+2. Springer-Verlag, 2013.
Bibliography
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| Francesca Caravenna, Paolo Dai Pra | Probabiltà - Un primo corso attraverso modelli e applicazioni (Edizione 1) | Springer-Verlag | 2013 |
Examination Methods
Written exam, with exercises and theoretical questions.
The assessment methods could change according to the academic rules
