# Aggregatore Risorse Aggregatore Risorse

Lecturers: P. Bazzurro, P. Venini

## Programma

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.

DESCRIPTION
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 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 Tutorial hours Tot From____ To____ From____ To_____ h 1 online 08-Feb 9:00-12:00 3 online 09-Feb 9:00-12:00 3 online 10-Feb 9:00-12:00 3 online 11-Feb 9:00-12:00 16:00-18:00 5 online 12-Feb 14:00-16:00 2 2 online 15-Feb 9:00-12:00 3 online 16-Feb 9:00-12:00 3 online 17-Feb 9:00-12:00 16:00-18:00 5 online 18-Feb 9:00-12:00 16:00-18:00 5 online/UNIPV 19-Feb 14:30-16:30 midterm exam 2 3 online 22-Feb 9:00-12:00 16:00-18:00 5 online 23-Feb 9:00-12:00 3 online 24-Feb 9:00-12:00 14:00-17:00 6 online 25-Feb 10:00-12:00 14:00-17:00 5 online 26-Feb 4 online 01-Mar 14:00-16:00 2 online 02-Mar 9:00-12:00 3 online 03-Mar online 04-Mar online/UNIPV 05-Mar 9:00-12:00 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

ASSESSMENT         % of Final Mark Documentation
Evaluation
Assignments 25% Open
Midterm Examination 25% Closed books and notes
Final Examination 50% Closed books and notes

Paolo Bazzurro

Professore Ordinario di Tecnica delle costruzioni

Ciclo :  XXXIII, XXXIV, XXXV, XXXVI

Tipologia corso : Caratterizzante

Curriculum : Ingegneria Sismica e Sismologia

Periodo: Semestre I