# 13863 - Mathematical Statistics Modulübersicht

 Module Number: 13863 Module Title: Mathematical Statistics Mathematische Statistik Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology Responsible Staff Member: Prof. Dr. rer. nat. Hartmann, Carsten Prof. Dr. rer. nat. habil. Wunderlich, Ralf Language of Teaching / Examination: English Duration: 1 semester Frequency of Offer: On special announcement Credits: 8 Learning Outcome: The students are skilled in probability theory,know the basic statistical models and learn how to correctly use statistical methodscan study advanced topics in stochasticsunderstand statistical methods thoroughly to avoid biased and false conclusionsare experienced in autonomously doing research based on specific applications. Contents: Descriptive statistics (central tendency and variation, quantiles, linear regression)Parameter estimation (point estimates, confidence intervals, Bayesian estimastion, sufficient statistic)Hypothesis testing (statistical tests, Neyman-Pearsonlemma, one- and two-sided tests)Linear models (regression and variance analysis, linear classification, Gauss-Markov theorem)Applications and use of statistical software Recommended Prerequisites: Knowledge of the content of module 11217: Probability Theory Mandatory Prerequisites: No successful participation in module 11331 - Mathematische Statistik. Forms of Teaching and Proportion: Lecture / 4 Hours per Week per Semester Exercise / 2 Hours per Week per Semester Self organised studies / 150 Hours Teaching Materials and Literature: G. Casella, R.L. Berger. Statistical Inference. Duxbury, 2002W.R. Pestman. Mathematical Statistics. De Gruyter 1998Jun Shao, Mathematical Statistics, Springer, 2003, DOI: 10.1007/b97553H.-O. Georgii, Stochastics: Introduction to Probability and Statistics, De Gruyter, 2008 (DOI: 10.1515/9783110206760) Module Examination: Prerequisite + Final Module Examination (MAP) Assessment Mode for Module Examination: Prerequisite:Successful completion of homeworkFinal module examination:Written examination, 90 min. OROral examination, 30 min.  In the first lecture it will introduced, if the examination will organized in written or oral form. Evaluation of Module Examination: Performance Verification – graded Limited Number of Participants: None Part of the Study Programme: Master (research-oriented) / Artificial Intelligence / PO 2022 Bachelor (research-oriented) / Informatik / PO 2008 - 1. SÄ 2017 Master (research-oriented) / Informatik / PO 2008 - 2. SÄ 2017 Bachelor (research-oriented) / Künstliche Intelligenz / PO 2022 Bachelor (research-oriented) / Mathematik / PO 2019 Master (research-oriented) / Physics / PO 2021 Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2019 - SÄ 2021 Remarks: Study programme Mathematics B.Sc.: Compulsory elective module in complex „Specialisation“Study programme Economathematics B.Sc.: Compulsory elective module in complex „Specialisation“Study programme Physics M.Sc.: Compulsory elective module in complex „Minor Subject“Study programme Computer Science B.Sc.: Compulsory elective module in „Applied Mathematics“ or in field of application „Mathematics“Study programme Computer Science  M.Sc.: Compulsory elective module in „Mathematics“ or in field of application „Mathematics“Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex  „Advanded Methods“Study programme Artificial Intelligence B.Sc.: Compulsory elective module in complex „Mathematics“ Module Components: Lecture: Mathematical StatisticsAccompanying exerciseRelated examination Components to be offered in the Current Semester: