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## Stochastics 2

 Module name (EN): Stochastics 2 Degree programme: Computer Science and Communication Systems, Master, ASPO 01.10.2017 Module code: KIM-STO2 Hours per semester week / Teaching method: 2V (2 hours per week) ECTS credits: 3 Semester: 2 Mandatory course: no Language of instruction: German Assessment: Written exam [updated 20.12.2017] Curricular relevance: KIM-STO2 Computer Science and Communication Systems, Master, ASPO 01.10.2017, semester 2, optional course, not informatics specific PIM-WI51 Applied Informatics, Master, ASPO 01.10.2011, semester 2, optional course, not informatics specific PIM-STO2 Applied Informatics, Master, ASPO 01.10.2017, semester 2, optional course, not informatics specific Workload: 30 class hours (= 22.5 clock hours) over a 15-week period.The total student study time is 90 hours (equivalent to 3 ECTS credits).There are therefore 67.5 hours available for class preparation and follow-up work and exam preparation. Recommended prerequisites (modules): KIM-STO1 Stochastics 1 [updated 12.01.2018] Recommended as prerequisite for: Module coordinator: Prof. Dr. Barbara Grabowski Lecturer: Prof. Dr. Barbara Grabowski [updated 10.11.2016] Learning outcomes: Based on Stochastics 1, this course will teach stochastic methods with a special focus on their applications in informatics. The lecture will focus on performance analysis methods (traffic theory) for discrete systems and the optimal coding of information.After successfully completing this module, students will be able to estimate unknown probabilities and parameters such as expected values and variances based on observation data and calculate how large the number of observations should be in order to ensure that the estimates comply with a given accuracy and safety probability They will be able to establish hypotheses about unknown distribution types and their parameters and to test them with the correct statistical methods.Students will be able to model complex discrete random systems using a simulation program and evaluate the simulation results statistically.      [updated 24.02.2018] Module content: 1.      Distributions of random variable functions1.1     Limit theorems 2.      Statistical inferences2.1     Sample size determination for estimating probabilities and averages2.2     Tolerance intervals and hypothesis tests2.3     Special hypothesis tests to determine distributions and compare probabilities         and averages 3.      Special applications in Informatics      3.1        Generation of random numbers3.2        Application of statistical methods in the simulation of discrete systems3.3     Queueing theory3.4        Applications in traffic measurement3.5     Statistical methods in information and coding theory [updated 24.02.2018] Teaching methods/Media: 50% of the lecture will take place in the PC lab AMSEL “Angewandte Mathematik, Statistik und eLearning”. Computer-supported practical case studies will be carried out here using the e-learning system OLAT:Statistik, R and ANYLOGIC.Students will become familiar with the AnyLogic simulation program and complete their homework and exercises using the systems mentioned above. [updated 30.07.2021] Recommended or required reading: KLIMANT, Herbert; PIOTRASCHKE, Rudi; SCHÖNFELD, Dagmar: Informations- und Kodierungstheorie, B.G.Teubner, Leipzig, 1996WARMUTH, Elke: Mathematische Modelle in der Simulation diskreter Systeme, ZFH Koblenz, 2002.GRABOWSKI, Barbara: Stochastik für Informatiker, e-Learning-Buch in OpenOLAT. [updated 24.02.2018] Module offered in: SS 2021, SS 2020, SS 2019, SS 2018
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