RISK AND UNCERTAINTY

This compulsory course explores formal tools to reason about chance and its properties. It course provides an introduction to probability theory, viewed as the scientific language to deal with risk and uncertainty. It emphasises an applied approach where probability is applied to problem solving.

Due to the cuts in teaching enacted by the Academic Senate (1 ECTS=3.75 actual hours of frontal instruction), this 6-ECTS course may cover less than what is customarily expected in similar courses taught across the European Union.

a) Knowledge and understanding:
a.1) Ability to interpret simple probabilistic statements.
a.2) Ability to think formally about chance.
a.3) Ability to recognize and use the most common probability distributions, both discrete and continuous.

b) Applying knowledge and understanding:
b.1) Ability to deal with simple combinatorial problems.
b.2) Ability to manipulate and use basic probability laws.
b.3) Ability to build formal models.

c) Making judgements
c.1) Ability to evaluate and compare basic situations based on risky events.

This course emphasizes both theory and applications. The formal prerequisite is successful completion of the first-year course in Mathematics.

Combinatorial probability.
General rules of probability.
Discrete random variables.
Continuous random variables.
Multivariate distributions.

A. Asimow and Mark M. Maxwell, Probability and Statistics with Applications: A Problem Solving Text, 2nd ed., 2015.

[Optional reading (in Italian): M. Li Calzi, La matematica dell'incertezza, Il Mulino, 2016.]

Grading is based on a final written exam, which may be supplemented by an oral exam within five working days of the written test.

The written exam consists of eight multiple-choice questions and two open problems. Each of the two parts is worth 16 points. It is mandatory to obtain at least 6 points in each part to pass the exam.
The exam is closed-notes and closed-book, but you may use a pocket calculator and both sides of an A4-sheet prepared by yourself at home.

After the written exam, a random sample of students is selected to take a short oral exam where they present and explain how how their answers were obtained. This oral exam is an integral part of the examination and is held within five working days of the written exam. Any student who does not show up for the oral exam is declared withdrawn; in this case, their exam is canceled and must be retaken in its entirety.

Finally, students who achieve a score no less than 30 on the written exam are offered the option to take an oral exam if they wish to try for honors (cum laude). This oral exam (held only upon request) assesses the ability to cross-reference and connect acquired knowledge to tackle more complex problems. It becomes an integral part of the exam and is held within five working days of the written exam. The score rom the written exam can either decrease or increase after the oral exam.

Failure to register for the exam is sufficient grounds for denying admission.

written and oral

The instructor is responsible for ensuring the authenticity and originality of all examinations and coursework. In cases of suspected academic misconduct, an additional on-site assessment may be required during the exams, which may differ from the standard format.

Grading is given in 30 out of 30. The minimum passing grade is 18/30 and the maximum grade is 30/30. The qualification “cum laude” may be added to the maximum grade.

Lectures and practice sessions.

For information and updates, see the class Moodle page.

Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding support services and accommodation available to students with disabilities. This includes students with mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). If you have a disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.