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IIn 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.

Probability and Statistics - Why bother? Estimation

Programma

IIn 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.

Programma

Subject
Overview of the course. Why do we need probability and statistics?
• Main objectives of the course
• Probability and Statistics. Why Bother? Do you have a good number sense?
Fundamentals of Applied Probability and Statistics
• Looking ahead: Examples of use of probability and Statistics to model occurrences of natural events Set Theory and Probability Theory
• Random Variables and Distributions- Jointly Distributed Random Variables
• Expectations and Moments of Random variables
• Using Empirical Data
• Common Probability Distribution Models: Models for Repeated Experiments
Fundamentals of Applied Probability and Statistics
• Common Probability Distribution Models: Models for Random Occurrences
• Limiting Cases: the Normal Distribution, the Lognormal Distribution, the Extreme Value Distributions (Part I)
Fundamentals of Applied Probability and Statistics
• Common probability distribution models:
Limiting cases: the Normal (Gaussian) distribution – the Lognormal distribution – Extreme Value Distributions (Part II)
• Uniform and Beta distributions
• Functions of Random Variables
Fundamentals of Applied Probability and Statistics
• Monte Carlo Simulation
• Overview of Applied Classical Statistics:
o Distribution Parameter Estimation
o Random Variable Model Selection
• Basics of Linear Regression Analysis

Paolo Bazzurro

Professore Ordinario di Tecnica delle costruzioni

Classe: Scienze tecnologie e Società

Ambito: Scienze e Tecnologie

Semestre: Semestre II