Course program
General objectives:
to acquire basic knowledge in probability theory.
Specific objectives:
Knowledge and understanding:
at the end of the course, students will be able to use basic notions in combinatorics to solve math problems, derive laws for discrete random variables.
Applying knowledge and understanding:
at the end of the course, students will be able to solve simple problems in discrete probability, problems concerning discrete random vectors and random numbers represented by continuous random variables. They will understand the role of indipendence and conditioning in discrete models and understand the meaning of some limit theorems, like the law of large numbers.
Critical and judgmental skills:
students will have the bases to analize and to build simple probabilistic models for physics, biology and technology, simulate discrete probability distribution, as well as the Gaussian distribution and understand the use of some elementry tools in statistics, like inference, sampling and simulation.
Communication skills:
ability to expose the contents of the course in the oral part of the test and in any theoretical questions present in the written test.
Learning skills:
the acquired knowledge will allow a study, individual or given in a course related to more specialized aspects of probability theory.
Prerequisites
Basics of set theory, logics and calculus (limits, continuity and derivation).
Books
Sheldon M. Ross - A first course in probability
Exam mode
The exam consists of two distinct parts: a written test (mandatory) and an oral exam (optional).
The written test consists of a series of theoretical questions and practical exercises designed to assess the student's skills on the topics covered in the course. The evaluation will focus more on the ability to apply theoretical concepts to concrete problems and on the clarity of expression, rather than on the correctness of calculations and solutions. The written test is mandatory and forms the main basis for the final grade. Notes and books are allowed, electronic devices are forbidden.
The oral exam is optional and can be taken by students who have passed the written test but wish to further deepen their understanding, with the possibility of improving their written test score. During the oral exam, the student will be asked to discuss and argue specific theoretical topics from the course, with particular emphasis on understanding and the ability to communicate concepts clearly and accurately.
Final Evaluation: The final grade will be based on the result of the written test, with the oral exam serving to modify the score obtained in the written test. If no oral exam is taken, the final grade will depend solely on the written test.
Lesson mode
The lectures are recorded in asynchronous mode. In addition to the recorded lectures, the instructor meets with students through webinars, where the topics covered in the lessons are discussed with a focus on solving practical problems. Problems are provided to students in advance of the webinars, during which some possible solutions are presented in synchronous mode. All materials are available on Moodle, along with additional exercise sets. Furthermore, the instructor and students actively participate in a Moodle forum for continuous discussion of lecture topics and any questions arising from individual study of the related material.
