508172 - PROBABILITY AND STATISTICS FOR ENGINEERING APPLICATIONS

courses

ID:

508172

Duration (hours):

51

CFU:

SSD:

TECNICA DELLE COSTRUZIONI

Year:

2025

Date/time interval

Primo Semestre (22/09/2025 - 24/10/2025)

Course Objectives

Many problems in Civil Engineering cannot be fully or efficiently addressed without a solid understanding of
probability and statistics. In this course, we aim to cover the fundamental concepts of probability and statistics
relevant to practical applications, minimizing discussions on topics like dice tossing and card games. Rather
than focusing on derivations, we will emphasize concepts and real-world applications. We will begin by
exploring how probability and statistics are related but distinct, followed by an introduction to random
variables and functions of random variables. Next, we will delve into probability distribution functions
commonly used in civil engineering. Towards the latter part of the course, we will discuss statistics and
sampling, including topics such as goodness-of-fit tests, regression analysis, parameter estimation, and
hypothesis testing. We will also introduce the basics of Monte Carlo simulation and variance reduction
techniques.
Each topic will be linked to practical problems and solutions across various civil engineering disciplines,
including Structural, Earthquake, Transportation, Water Resources and Environmental, and Geotechnical
Engineering. Basic decision analysis applications will also be introduced.

Course Prerequisites

Knowledge of college-level calculus and basic skills in at least one of the following computer SW tools:
Excel, Matlab, R. Proficiency in reading, writing and comprehending English language. Examples from
different branches of engineering will be used throughout the course, but no prior in-depth knowledge of
engineering is necessary.

Teaching Methods

Theoretical lessons and exercise, all of which are taught in person

Assessment Methods

Assignments 20%, with Open Documentation.
Final Examination 80% with closed books and notes.

Texts

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.

Theoretical lectures will be supplemented with tutorials, focusing on the practical application of the
concepts and methods introduced during the lectures. The topics covered in the course are outlined
below:
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