NumberdistECTS3.0LevelintermediateOverviewThis course deals with models of probability and statistics suitable for modeling random processes like lottery, roulette, waiting queues, polls etc. These models allow for predictions and estimations either with exact calculations or with the help of computerized simulation.
Topics
(The order and the emphasis are left to the lecturer)
- A. Elementary probability theory and combinatorics
Random events, Laplace probability space, combinatorics, Kolmogorov’s axiom system, conditional probability, statistical independence, Bayes’ rule
- B. Random variables and discrete distributions
Random variables, expectation value, variance, binomi-al/Poisson/geometric/hypergeometric distribution,
- C. Aspects of continuous distributions
Normal/exponential distribution
- D. Generating of random numbers and simulation
Linear congruential generator, Inverse transform sampling, Monte-Carlo-simulation
- E. Discrete Markov processes
Markov chain, transition matrix, transition graph, stationary probability
- F. Queueing theory
Kendall’s notation, properties of M|M|s|c-queues, simulation
- G. Aspects of descriptive statistics
Median, quartiles, Box plot
Learning objectives
- The students know the mathematical foundations for describing random events: probabilities, Laplace probability space, combinatorics, random variables, distributions, expectation value, variance, standard deviation
- They know the main distributions and which processes can be modeled with these distributions.
- They know how random numbers may be generated and how computer-ized simulation works.
- They know what a (homogenous) Markov chain is. They are able to model such chains with transition matrices and transition graphs. They are able to determine the long term behavior of a Markov chain.
- They know models for waiting queues and are able to determine proper-ties like the mean waiting time of such queues via exact computations or simulation.
- They are able to compute and interpret the main statistical measures
.
Previous knowledgeMathematical foundations of computer science (mgli)
Linear algebra und geometrie (lag)
Introduction to analysis (eana)
Exam formatContinuous assessment grade with final written exam 
