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Basic Statistics and Probability Theory
Statistik und Wahrscheinlichkeitsrechnung
Last Updated: 2026-02-05 15:10:38
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
To provide an introduction on basic statistics, probability theory and uncertainty modeling in the context of engineering decision making. Some emphasis is given to the aspects of probabilistic model building, hypothesis testing and model verification to facilitate a consistent treatment of uncertain information in the development of engineering decision basis. Basic tools are introduced for assessing probabilities as needed in risk analysis. Finally the concepts of decision theory are provided and it is explained how these provide the basis for engineering decision making subject to uncertainty.
Content
Presentation of typical engineering decision problems involving statistics and probability in the field of civil, surveying and environmental engineering. Descriptive statistics, graphical representations, sample moments, linear correlation Random events, sample spaces, axioms of probability, probability of an event, probability of an union, conditional probability Discrete vs continuous variables, PMF/PDF, CDF, marginal and conditional distribution, joint probability distribution Moments of a random variable, expectation of a function of a r.v., properties of expectation, conditional expectation, expectation of jointly distributed random variables Discrete random trials, repeated trials, return period, models from random occurrences (Poisson, exponential, gamma), central limit theorem. Models from limiting cases (Normal, Lognormal, Extreme value distribution). Properties of estimators, probability distribution functions in statistics, estimators for sample descriptors – statistics. Testing for statistical significance, selection of distribution function, probability paper. Estimation of distribution parameters, methods of moments, maximum likelihood method. Model evaluation by testing, Chi-square tests, Kolmogorov-Smirnov test. Bayesian estimation methods, Bayesian regression Error propagation, first order reliability methods, Monte Carlo simulation Introduction to event and decision trees, concept of risk, prior, posterior and pre-posterior analysis.
Resources
Lecture Notes
Lecture Notes:Faber, M.H., "Risk and Safety in Civil, Geomatics and Environmental Engineering", Version May2004.
Literature
Additional references are provided in the Lecture Notes
General Information
- Language
- English
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 120 minutes
- Aids
- Alle Unterlagen (Skripte, Bücher, andere Ausdrucke, etc.) erlaubt. Taschenrechner (nicht programmierbar, ohne Kommunikationsmittel) erlaubt. Keine Kommunikationsmittel (z.B. Natel).
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Statistics and Probability Theory |
|
4 h weekly |