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
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea in Matematica applicata - Enrollment from 2025/2026The 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. 2021/2022
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3° Year activated in the A.Y. 2022/2023
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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 (2021/2022)
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 aim of the course is to introduce the basic concepts of probability and mathematical statistics, adding concrete applications to mathematical rigor. Basic notions at the core of inferential Statistics will be also rigorously introduced, together with relevant case studies.The ultimate goal is to provide the student with the tools to be able to understand and apply rigorously, and in complete autonomy, the calculus of probability and statistics to various problems, suggested by both science and daily life. This includes the ability to analyze data, evaluate its qualitative properties to choose suitable models through an abstraction process, and the ability to read texts and articles.
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. Hypothesis testing. Significance and power of a test. Most powerful tests. Neyman-Pearson tests for simple and unilateral hypothesis. Tests for mean and variance of normal samples.
Textbook: Q. Berger, F. Caravenna, P. Dai Pra, Probabilità. Un primo corso attraverso esempi, modelli e applicazioni - UNITEXT - La matematica per il 3+2. Springer-Verlag, 2021 (Ed. 2).
Bibliography
Examination Methods
To pass the exam, students must show:
- to have assimilated the theoretical notions, showing detailed knowledge of definitions and statements, as well as of some proofs;
- to be able to apply theory to problem solving.
The exam consists of a 180-minute written test which includes a theoretical part, with at least one proof required, and a part of exercises.
The assessment methods could change according to the academic rules
