PROBABILITY AND STATISTICS-1

This is a compulsory course for the Bachelor's Degree Programme in Informatics, contributing to the quantitative skills of the students. The specific aim is to provide familiarity with the main probabilistic methods used in the context computer sciences.
The course provides elements of probability theory, the use of specific programs for probabilistic calculus, simulation and reporting.
At the end of the course, the students will be able to identify suitable models and methodologies in the context of interest; moreover they will learn to interpret and communicate the obtained results.

1. Knowledge and understanding capacity:
- of the basic concepts of elementary probability, probability distributions and limit theorems
- of the main tools for calculation and graphical representation of univariate and bivariate probability distributions
- of the principles and practical importance of Markov chains

2. Ability to apply knowledge and understanding:
- to use specific programs for simulation and probability distribution manipulation
- to use appropriate formulas and terminology for the application and communication of the acquired knowledge

3. Independence of judgment:
- to apply the acquired knowledge in a specific context, independently identifying the most appropriate probabilistic models and methods

4. Communication skills:
- to present in a clear and exhaustive way the results obtained from the solution of a probability problem, using rigorous formulas and appropriate terminology

5. Learning skills:
- to use and merge information from notes, books, slides and practical sessions
- to assess the achieved knowledge through quizzes, exercises and assignments during the course

Knowledge of mathematics at the level of the first year courses: Calculus (1 and 2) and Linear Algebra. In particular, differentiation and integration of functions of one or two variables, and solving simple linear systems of equations.

Probability:
- Sample space, events and the axioms of probability
- Conditional probability and independence
- Discrete and continuous random variables
- Expectation and moments
- Some families of distributions and the Poisson process
- Joint distributions of random variables, covariance and correlation
- Convergence of random variables and limit theorems
- Markov chains

The use of the software R (http://cran.r-project.org/ ) is part of the programme of the course and the main tool for solving the assignments.

Main textbook:
Introduction to probability for Computing (2024) Mor Harchol-Balter. Cambridge University Press. (Available online: https://www.cs.cmu.edu/~harchol/Probability/book.html )

Other suggested books:
Introduction to probability models (2010) Ross, Sheldon M. Academic Press
Introductory Statistics (2010) Ross, Sheldon M. Academic Press
Introduction to Probability and Statistics for Engineers and Scientist (2014) Ross, Sheldon M. Academic Press
A first course in probability (2010) Ross, Sheldon M. Pearson Prentice Hall, 2010
Probability and statistics for computer scientists (2014) Baron, Michael Chapman & Hall/CRC
Probability with Applications in Engineering, Science, and Technology (2017) Carlton, Matthew A. and Devore, Jay L. Springer, Cham

Course Evaluation Method:
The assessment for the entire course is a written exam consisting of two partial exams. Each partial exam is worth a maximum of 31 points and lasts 90 minutes.
To pass the course, students must achieve a sufficient score in each of the two partial exams, meaning at least 18 points in each.
- Sequential Requirement: Only students who have passed the first partial exam are eligible to take the second.
- Full Exam Option: It is possible to take the complete exam by performing both partials on the same day, but strictly in succession. If the score for the first partial is insufficient, the second partial will not be graded.
- Validity: Both partial exams must be passed within the same academic year. Once the first partial is passed, the score remains valid for the remaining exam sessions of that academic year only, until the second partial is passed.
- Final Grade: Once both partial exams are passed, the final grade will be the average of the two scores. An overall score exceeding 30 points corresponds to a grade of cum laude (lode).

Instructions for the First Partial Exam:
The first partial exam will cover the material of Module 1 only. The use of R is an important part of the course and will be subject to evaluation through the adequate use of commands in the written exam.
The exam will be composed of the following:
- One open question on theory (5 points): Evaluation will focus on the clarity, completeness, correctness, and conciseness of the response.
- Six single-choice questions (1 point each): Only the final answer will be marked; no justification or procedure trace is required.
- Three exercises (7 points each): A justification is required and carries a higher value than the final numerical answer. Clarity and order will also be taken into consideration during grading.
- Exam Rules:
+ Closed book exam: However, a formulary is allowed. Each student is responsible for their own formulary, which must be completely contained on both sides of one A4 sheet.
+ An adequate calculator is required. It is the student's responsibility to bring a functioning calculator and to know how to use it.

written

Regarding the grading scale (for attending and non-attending students alike), exam grades will depend on the level of the capabilities shown:
- Sufficient (18-22 points): to students who demonstrate a sufficient theoretical knowledge base and capacity to apply the concepts covered throughout the course, as well as a sufficient capacity to elaborate and present results using the specific language and mathematical notation associated to probability models and their interpretation
- Good (23-26 points): to students who demonstrate a good theoretical knowledge base and capacity to apply the concepts covered throughout the course, as well as a good capacity to elaborate and present results using the specific language and mathematical notation associated to probability models and their interpretation
- Very good (23-26 points): to students who demonstrate a very good superior theoretical knowledge base and capacity to apply the concepts covered throughout the course, as well as a very good or superior capacity to elaborate and present results using the specific language and mathematical notation associated to probability models and their interpretation and at least a basic capacity to identify relations between different concepts covered throughout the course and formulate independent judgement.
- Honors will be granted to students exhibiting an excellent knowledge base anc capacity to apply the concepts covered during the course through the use of specific language and mathematical notation, including the identification of relationships between different concepts and definitions.

Theoretical lectures and exercises at the blackboard and with PC using R. Use of the Moodle platform for learning assessment during the course.