PROBABILITY AND STATISTICS

The course is one of the quantitative training activities of the Bachelor's Degree Programme in Informatics. The aim is to get the student familiar with the main probabilistic methods for use in computer science.
The course provides knowledge of probability, as well as skills in the use of specific programs for probabilistic calculus, simulation and reporting.
At the end of the course, the student will be able to identify suitable models and methodologies in the context of interest; moreover he will learn to interpret and communicate the obtained results on simple reports.

1. Knowledge and understanding:
- to know the basic concepts of elementary probability, probability distributions and limit theorems
- to know the main tools for calculus and graphical representation of one-dimensional and multivariate probability distributions
- to know and understand the practical importance of Monte Carlo simulation methods

2. Ability to apply knowledge and understanding:
- to use specific programs for working with probability distributions and for simulation
- to use appropriate formulas and terminology in all the processes of application and communication of the acquired knowledge

3. Ability to judge:
- 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 solving 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 and Discrete mathematics.

Probability: sample space, events and 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; simulation and Monte Carlo methods.
The use of the software R (http://cran.r-project.org/ ) is part of the programme of the course and is tested in the exam.

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). Probabilita' 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 (2016). Calcolo delle probabilità. Terza edizione. Apogeo.
S.M. Ross (2015). Probabilità e statistica per l'ingegneria e le scienze. Terza edizione. Apogeo.

The achievement of the course objectives is assessed through participation in activities and assignments during the course and a written final exam.
The final exam (30 points) is composed by exercises similar to those solved or assigned during the course.
The use of the software R is part of the program of the course and included in the written exam. Examples of quizzes and exercises will be available in Moodle.
Activities and assignments consist on the solution of quizzes and exercises proposed in Moodle. The solution to some exercises is in the form of short reports.
A further bonus of 3 points can be added to the final grade for those students that participate in the activities and quizzes assigned during the classes.

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

Italian

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