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 lab sessions
- to assess the achieved knowledge through quizzes, exercises and assignments during the course

Knowledge of mathematics at the level of Calculus 1 and 2

Probability:
- Sample space, events and the axioms of probability
- Conditional probability and independence
- Discrete and continuous random variables
- Expectation and moments
- 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:
S.M. Ross (2004). Calcolo delle probabilità. Apogeo.

Other suggested books:
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 participation in activities and assignments during the course together with a written final exam.

The written final exam has a value of 30 points. The exercises and questions are similar to those solved during the course or included in Moodle.
During the exam, the use of formulary and distribution tables. A 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

Students taking part in the class quizzes (in presence only) may accumulate up to 4 extra points, to be added to the final written exam mark. 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.

Italian

written