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Module description - Discrete Stochastics
(Diskrete Stochastik)

ECTS 3.0
Level intermediate
Overview This 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.


    (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 knowledge
  • Mathematical foundations of computer science (mgli)
  • Linear algebra und geometrie (lag)
  • Introduction to analysis (eana)
  • Exam format Continuous assessment grade with final written exam
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