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Statistics and Probability Theory
Last Updated: 2026-02-05 15:19:09
Abstract
Introduction on basic statistics, probability theory and uncertainty modeling in the context of engineering decision making. Emphasis is given to the aspects of probabilistic model building, hypothesis testing and model verification. Basic tools are introduced for assessing probabilities as needed in risk analysis. Finally the concepts of decision theory are provided.
Objective
The aim of the present course is to provide to the students the basic tools of statistics and probability but with an emphasis on the application and the reasoning behind the application of these disciplines within the scope of engineering risk assessment and decision making.
Content
The course has been subdivided into the following seven modules, each consisting of one or more lectures: Module A - Engineering decisions under uncertainty Risk, events, probability and consequences. Module B - Basic probability theory Basics of set theory, definitions of probability, axioms of probability theory, probabilities of intersections and unions, conditional probabilities, the rule of Bayes. Module C - Descriptive statistics Graphical representations (histograms, scatter diagrams, quantile plots, Tukey box plots, quantile quantile plots, Tukey mean difference plots), numerical summaries (central measures, dispersion measures, skewness, peakedness and correlation). Module D - Uncertainty modelling Epistemic uncertainties, aleatory uncertainties, random variables, discrete and continuous probability distribution functions, moments, distribution parameters, properties of the expectation operator, jointly distributed random variables, functions of random variables, the central limit theorem, typical distribution functions in engineering, random processes, random sequences, extreme value distributions, return periods. Module E – Estimation and model building Probability distributions in statistics, statistical significance, confidence intervals, hypothesis testing, selection of distribution models, probability paper, parameters estimation, method of moments, method of maximum likelihood, model verification and comparison. Module F – Methods of structural reliability Limit state functions, basic random variables, failure criteria, safety margin, linear safety margins, the error accumulation law, First Order Reliability Methods, non-linear safety margins, Monte Carlo simulation. Module G – Bayesian decision analysis Expected utility, decision/event trees, prior, posterior and pre-posterior decision analysis, decision analysis in engineering risk assessment.
Resources
Lecture Notes
Lecture Notes:Faber, M.H., "Basic Statistics and Probability Theory", Version February 2007.
Literature
Additional references are provided in the Lecture Notes.
General Information
- Language
- English
- Levels
- BSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 120 minutes
- Aids
- Alle Unterlagen (Skripte, Bücher, weitere Ausdrucke, etc.) sowie Taschenrechner ohne Kommunikationsmöglichkeit erlaubt. Keine Kommunikationsmittel (Natel, WLAN, etc.).
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Statistics and Probability Theory |
|
4 h weekly |