Probability and Statistics for Engineering Applications
Term: 2ndSemester – Academic Year 2017-2018
Institution: UNIPV (DICAR) and IUSS
SSD: ICAR/09 Tecnica delle costruzioni – Structural Engineering
Duration: 4 weeks
Office hours: by appointment
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 a analyses, 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 organized will be taught in English.
Theoretical lectures will be complemented by tutorials(aiming at the practical application of the concepts and methods developed during the lectures). The topics that will be discussed in the course are reported in the following.
|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:
o Models for Repeated Experiments
o Models for Random Occurrences
o Limiting Cases: the Normal Distribution, the Lognormal Distribution, the Extreme Value Distributions
o 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
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.
- 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 beyond 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.
|Evaluation||% of Final Mark||Documentation|
|Midterm Examination||25%||1 sheet A4 (provided)|
|Final Examination||50%||2 sheets A4 (provided)|