OVERVIEW

The course provides an introduction to probability theory and statistics through applications typical of civil and environmental engineering. The course is divided equally into traditional lessons and computer laboratories in which the student learns to deal with realistic problems involving quantities affected by uncertainties.

AIMS AND CONTENT

LEARNING OUTCOMES

The course introduces the theory of probability and statistics as tools for the representation and analysis of random phenomena typical of the field of study. The mathematical bases of the discipline are defined starting from the general definitions to arrive at operative tools in order to represent and manipulate random or uncertain quantities. The discussion is supported by examples that cover the spectrum of applications foreseen in the following courses. Applications are performed on the computer using the Matlab programming environment.

AIMS AND LEARNING OUTCOMES

The course has two complementary educational objectives.

The first objective concerns the understanding of the fundamentals of probability theory and statistics. Students will learn the general mathematical framework necessary to clearly formulate the problems addressed, as well as the mathematical tools capable of representing and handling quantities affected by uncertainty. They will be taught to understand the general criteria for making decisions in contexts where the available data are uncertain or the amount of information is limited. Following this introduction, the course will present a series of typical applications in civil and environmental engineering, introducing problems that students will encounter in later courses and framing them within the common context of probability theory.

The second educational objective is to acquire the computing tools necessary to implement the mathematical techniques and concretely solve the addressed problems. To this end, students will learn both basic and advanced concepts in programming and in solving probabilistic problems related to civil and environmental engineering using the Matlab environment.

PREREQUISITES

There are no specific requirements

TEACHING METHODS

Lectures at the blackboard with the use of projections.

Classroom exercises: the instructor works through computer-based exercises together with the students.

Students with valid certifications for Specific Learning Disorders (SLDs), disabilities or other educational needs are invited to contact the teacher and the School's contact person for disability at the beginning of teaching to agree on possible teaching arrangements that, while respecting the teaching objectives, take into account individual learning patterns. Contacts of the School's disability contact person can be found at the following link Comitato di Ateneo per l’inclusione delle studentesse e degli studenti con disabilità o con DSA | UniGe | Università di Genova

SYLLABUS/CONTENT

Probability theory

Fundamentals. Events and sample space; probability: fundamental definitions and theorems; conditional and compound probability.

Random variables. Probability distribution; probability function (of a discrete random variable); probability density (of a continuous random variable); expected value; statistical moments of a random variable; linear transformations of random variables; statistically independent random variables; correlation and covariance.

Models of random variables. Normal, uniform, log-normal distribution, Rayleigh, Weibull.

Successions of random variables. Bernoulli sequence, binomial distribution, geometric model. Average return period.

Random occurrences, Poisson process, exponential model.

Asymptotic distributions, Gumbel model.

Statistics

Descriptive statistics, distribution indices, fractiles.

Estimated expected value, statistical moments, and probability density through the application of the frequentist definition of probability.

Order statistics method for estimating the probability distribution and the fractiles.

Estimation of the parameters of the distribution by means of the moment method, the method of maximum likelihood and the linear regression method in the probability paper.

RECOMMENDED READING/BIBLIOGRAPHY

Course notes available on Aulaweb

Kottegoda, N.T., and Rosso, R. (2008). Applied Statistics for Civil and Environmental Engineers, Blackwell Publishing Ltd

Ross S.M. (2015). Probabilità e statistica per l'ingegneria e le scienze. Maggioli SpA

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

https://corsi.unige.it/corsi/11949/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Practical test (computer) and oral exam

ASSESSMENT METHODS

The written test takes place in the classroom and consists in solving an assigned problem using Matlab, using the theoretical and IT tools described during the course.

The oral exam will focus on the theoretical topics covered during the course.

FURTHER INFORMATION

Ask the professor for other information not included in the teaching schedule