PROBABILITY AND STATISTICS

This mandatory Computer Science course equips students with the fundamental tools of probability theory used across various computing disciplines. Achieving the course's learning objectives will enable students to acquire the indispensable groundwork for understanding advanced computer science and data science methodologies rooted in probability.

Regular and active participation in the teaching activities and individual study will allow students to:
1. (knowledge and understanding)
-- know and understand basic concepts of probability calculus, the main probability distributions, and fundamental limit theorems
2. (applying knowledge and understanding)
-- describe phenomena characterized by variability and uncertainty
-- competently use specific statistical software for calculating and simulating probability distributions
3. (making judgements)
-- critically interpret the probabilities of events calculated analytically or derived from data analysis software

It is assumed that students have consolidated the mathematical competencies from the first year of the program. Specifically, mastery of differential and integral calculus for functions of one and two variables, understanding of limits and series sums, and the ability to solve simple systems of linear equations are required.

The course program includes presentation and discussion of the following topics:

1. Elementary probability (sample space, events and axioms of probability, combinatorial calculus, conditional probability, and independence)
2. Discrete random variables (distributions, moments, properties, and main families)
3. Continuous random variables (distributions, moments, properties, and main families)
4. Limit theorems (Law of Large Numbers, Central Limit Theorem)
5. Introduction to stochastic processes (Poisson process, Markov chains)

The methods will also be illustrated through simulations using the R language (www.r-project.org).

- Harchol-Balter M (2024). Introduction to probability for Computing. Cambridge University Press. (Disponibile online: https://www.cs.cmu.edu/~harchol/Probability/book.html )
- Baron M (2019). Probability and Statistics for Computer Scientistis. Third Edition. CRC Press.
- Readings and supplementary materials distributed during the course via the Moodle platform.

The achievement of the course objectives is assessed through a written exam. The exam consists of two parts. Each part consists of two exercises. The four exercises are designed to measure
1. the theoretical knowledge of the topics of the course,
2. the ability to apply the theory to solve problems.

The maximum score for each exercise is 8 points. The final score is given by the sum of the scores of the four exercises. To pass the exam it is necessary to obtain a sufficient score in each of the two parts, i.e. at least 9 points for each part. If the first part is not sufficient, then the second part of the exam will not be corrected. An overall score exceeding 30 points corresponds to honours.

During the exam, students are permitted to use a formula sheet provided by the instructor and a calculator. Books, notes, or other electronic devices are not allowed.

There will be an intermediate exam after the middle of the course. The intermediate test corresponds to the first part of the exam (two exercises). If the intermediate test is passed (with a score of at least 9 points) the student will be able to take only the second part of the exam during the first session (**only the first session**) and the final score will be given by the sum of the score obtained in the intermediate test and the score obtained in the second part of the exam of the first session.

written

The exam result is graded as follows:
- sufficient (18-22 points), if the student demonstrates a sufficient knowledge and understanding of the course methods, is able to apply and interpret them adequately, and uses technical terminology correctly;
- fair (23-25 points), if the student shows a good knowledge and understanding of the course methods, applies and interprets them convincingly, and uses technical terminology with fair accuracy;
- good (26-28 points), if the student possesses a solid knowledge and understanding of the course methods, applies and interprets them in a thoroughly convincing manner, and employs technical terminology accurately;
- excellent (29-30 points), if the student demonstrates an excellent knowledge and understanding of the course methods, applies and interprets them brilliantly, and uses technical terminology with extreme accuracy.

Distinction (lode) is reserved for students who, in addition to correctly solving all exercises, complete them with meticulous precision in every mathematical aspect.

Conventional theoretical lectures complemented by exercises and discussion of case studies. Teaching material prepared by the teacher will be distributed during the course through the Moodle platform. The statistical software used in the course is R (www.r-project.org).