2 nd Lecture: Review of Basic Probability Theory and Statistics
Aim of the present lecture
The aim of the present lecture is to review the basic theory of probability and statistics
together with uncertainty modelling and engineering model building. It is assumed that the
material of the present lecture in principle is already known to the students and that is why the
present lecture is only provided in a very condensed summary form. For the students who
require more background information it is suggested to have a look at the lecture notes for the
course on Basic Theory of Probability and Statistics in Civil Engineering. These are available
upon request from Annette Walzer ([email protected]).
On the basis of the lecture it is expected that the students should obtain an overview and a re-
freshened basic knowledge in regard to:
Which are the different interpretations of probability?
What is Bayes’ rule, and how can it be interpreted?
How can Bayes’ rule be applied for probability updating?
What is the purpose of descriptive statistics?
Which are possible numerical summaries and graphical representations?
What types of uncertainties are underlying engineering models?
How to represent uncertainties probabilistically?
What is a random variable and how may it be characterized?
What is a random process and what can it model?
How to model extreme events?
What is a return period?
How to develop engineering models based on data and experience?
How to select an appropriate probability distribution function?
How to estimate the parameters of a probability distribution function based on data?