# Aggregatore Risorse Aggregatore Risorse

## Programma

OBJECTIVES
Most problems in the different fields of Civil Engineering cannot be fully and efficiently addressed without knowledge of probability and statistics. In this course we will make an attempt to cover some basic aspects of probability and statistics that relate to practical matters keeping dice tossing and card games to a bare minimum. Less emphasis will be given to derivations and more to concepts and applications. We will start by discussing why probability and statistics are related but are not the same. Concept and definition of random variables and different functions of random variables will be covered in this initial part of the course. Afterwards, focus is given to commonly used probability distribution functions in civil engineering. Discussions on statistics and sampling are presented towards the last part of the course. In this part, goodness of fit tests, regression analysis, estimation of distribution parameters from statistics, hypothesis testing and their significance will be discussed. Finally basics of Monte Carlo simulation and an introduction to variance reduction techniques will also be covered. Each topic is discussed with reference to different application problems and their solutions in different fields of civil engineering, such as Structural Engineering, Earthquake Engineering, Transportation Engineering, Water Resources and Environmental Engineering, and Geotechnical Engineering. Basic applications of decision analysis will also be introduced.
The course will be taught in English.

Theoretical lectures will be complemented by tutorials (aiming at practical application of the concepts and methods developed during the lectures). The topics to be discussed in the course are reported in the following.

Course contents:

 Part Subject PART I Overview of the course. Why do we need probability and statistics? Fundamentals of Applied Probability and Statistics Main Objectives of the Course Probability and Statistics. Why Bother? Do you have a good number sense? Looking ahead: Examples of use of probability and Statistics to model occurrences of natural events PART II Fundamentals of Applied Probability and Statistics Set Theory and Probability Theory Random Variables and Distributions Jointly Distributed Random Variables Expectations and Moments of Random variables Functions of Random Variables Using Empirical Data Common Probability Distribution Models:   Models for Repeated Experiments Models for Random Occurrences Limiting Cases: the Normal Distribution, the Lognormal Distribution, the Extreme Value Distributions Uniform and Beta distributions Part III Monte Carlo Simulation Brute-force Monte Carlo simulation Variance-reduction techniques Part IV Overview of Applied Classical Statistics: Distribution Parameter Estimation Random Variable Model Selection Goodness of fit tests Basics of Linear Regression Analysis Hypothesis testing

## Svolgimento

 Week Classroom Date Lecture hours From____ To____ Tutorial hours From____ To_____ Tot h 1 IUSS, 1-17 03/02/2020 14.00 – 17.00 3 IUSS, 1-17 04/02/2020 10.00 – 12.00 14.00 – 16.00 4 IUSS, 1-17 05/02/2020 10.00 – 12.00 14.00 – 16.00 4 IUSS, 1-17 06/02/2020 16.00 – 18.00 2 IUSS, 1-17 07/02/2020 09.00 – 12.00 14.00 – 16.00 5 2 IUSS, 1-15 10/02/2020 09.00 – 12.00 3 IUSS, 1-15 11/02/2020 10.00 – 12.00 14.00 – 16.00 4 IUSS, 1-15 12/02/2020 09.00 – 12.00 16.00 – 18.00 5 IUSS, 1-17 13/02/2020 16.00 –  18.00 2 IUSS, Sala del Camino 14/02/2020 14.30 – 16.30 Midterm Exam 2 3 IUSS, Sala del Camino 17/02/2020 09.00 – 12.00 16.00 – 18.00 5 IUSS, 1-15 18/02/2020 09.00 – 12.00 3 IUSS, 1-15 19/02/2020 10.00 – 12.00 13.00 – 16.00 5 IUSS, 1-15 20/02/2020 10.00 – 12.00 13.00 – 16.00 5 4 IUSS, 1-15 24/02/2020 14.00 – 16.00 2 IUSS, 1-15 25/02/2020 09.00 – 12.00 3 IUSS, Sala del Camino 28/02/2020 09.00 – 12.00 Final Exam 3

## Bibliografia

Handouts, scientific papers and other technical materials made available during the course.
Although not required, the following books may prove to be very useful for the course and as future reference after the course

• Ang, A. H. and Tang, W. H. (2007). “Probability Concepts In Engineering: Emphasis On Applications In Civil & Environmental Engineering,” Wiley.
• Benjamin, J. R. and C. A. Cornell (1970). Probability, Statistics, and Decision for Civil Engineers. New York, McGraw-Hill.
• Kutner M.H., Nachtsheim C., and Neter J., 2004. Applied linear regression models, McGraw-Hill, 1396 p.

## Esame

 Evaluation % of Final Mark Documentation Assignments 25% Open Midterm Examination 25% 1 sheet A4 (provided) Final Examination 50% 2 sheets A4 (provided)

Paolo Bazzurro

Professore Ordinario di Tecnica delle costruzioni

Ciclo :  XXXIII, XXXIV, XXXV

Tipologia corso : Caratterizzante

Curriculum:  Ingegneria Sismica e Sismologia; Rischi Idrometeorologici, Geologici, Chimici ed Ambientali

Periodo: Semestre I