Probability Modelling

Probability is the basis for describing and modelling randomness and uncertainty in the world. Starting from probability concept, random events and random variables, students acquire tools to understand an make statements about random events.

Students understand the concepts of random event, set operations with random events, and independence of events. They understand conditional probability and Bayes' theorem. They can formulate random experiments and events, use data data or other knowledge and determine event probabilities.

The students know the tool of random variables and can use it for modelling. They know the most important discrete and continuous distribution families and know in which characteristic situations they apply. Expected value and variance of a random variable can be calculated and interpreted.

Students identify a suitable distribution family for a variable based on data and can make statements about the parameters of the population based on samples. They can determine confidence intervals for parameter estimates.

Students can formulate a hypothesis about a population and test the hypothesis with sample data. Students know the most important statistical test procedures and can use them specifically in practical applications.

Students can apply Monte Carlo simulations to analyze non-trivial behavior of systems and determine the probability of events therein.