PROBABILITY AND STATISTICS

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:
- 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. Ability to discern:
- to apply the acquired knowledge in a specific context, 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. (Disponibile online: https://www.cs.cmu.edu/~harchol/Probability/book.html )

Other suggested books:
S.M. Ross (2004). Calcolo delle probabilità. Apogeo.
M. Boella (2011). Probabilità e statistica per ingegneria e scienze. Pearson Italia, Milano.
G. Espa, R. Micciolo (2014). Problemi ed esperimenti di statistica con R. Apogeo.
H. Hsu (2011). Probabilità, variabili casuali e processi stocastici. McGraw-Hill.
R.A. Johnson (2007). Probabilità e statistica per ingegneria e scienze. Prentice Hall.
W. Navidi (2006). Probabilità e statistica per l'ingegneria e le scienze. McGraw-Hill.
S.M. Ross (2003). Probabilità e statistica per l'ingegneria e le scienze. Apogeo.

Achievement of the course objectives is evaluated through a written final exam with a maximum value of 30 points to be solved in 90 minutes. The exercises and questions are similar to those solved during the course or included in Moodle. A mock exam and some exams for the past academic year will be available on the Moodle page for the course.
During the exam, the use of formulary and distribution tables. A (scientific) calculator is also needed.
The use of the software R is an essential part of the program and is subject to examination.
Further details on Moodle.

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.

Students may improve their final grade (iup to a maximum of 4 extra points, to be added to the final written exam mark) thorough substantial and continuative work during the course. Such work will be evaluated through the (non-mandatory) participation, exclusively in presence, to quizzes (on Moodle and about 10-25 minutes long) on pre-defined dates (to be published on Moodle during the first two weeks of lessons). Any extra points earned remain valid for all 4 exams of the academic year, but are lost and no longer valid for future exams if the student renounces a passing grade.

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

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