M4122 Probability and Statistics II

Faculty of Science
Spring 2004
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ladislav Skula, DrSc. (lecturer)
RNDr. Marie Forbelská, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ladislav Skula, DrSc.
Timetable of Seminar Groups
M4122/01: Tue 9:00–10:50 UM, M. Forbelská, 2.r. M
M4122/02: Tue 7:00–8:50 UM, M. Forbelská, 2.r.Me,Mb
Prerequisites
M3121 Probability
Differential and integral calculus of functions of n real variables. Basic knowledge of linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The basic course of probability and mathematical statistics and introductory course for other theoretically oriented and applied stochastic subjects. The content of the course is an introduction to mathematical statistics, theory of estimation and the principle of statistical hypotheses testing. The course is oriented to random samples from normal distributions.
Syllabus
  • Random samples: definition and sample characteristics, unbiased and consistent estimators, samples from normal populatins, examples of point and interval estimators. Theory of estimation: the best unbiased estimators, sufficient statistics, Rao-Blackwell theorem, efficient estimators, methods for construction of point estimators (maximum likelihood method, moment method, Bayessian estimation, minimum Chi-square estimation, quantiles and methods for interval estimation. Statistical hypotheses testing: basic concepts, testing based on confidence intervals, Neyman-Pearson lemma, likelihood ratio tests, tests on parameters of normal distributions, tests based on central limit theorem, goodness-of-fit tests
Literature
  • Hogg, R.V. and Craig, A.T. Introduction to mathematical statistics. Macmillan Publishing. New York. Fourth editionn. 1978
  • MICHÁLEK, Jaroslav. Úvod do teorie pravděpodobnosti a matematické statistiky. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1984, 204 s. info
  • Stuart, A., Ord, K. and Arnold, S. Kendall's Advanced theory of statistics. Vol.1,2A, Arnold, London,1999
  • Dupač, V. a Hušková, M.: Pravděpodobnost a matematická statistika. Karolinum. Praha 1999.
Assessment methods (in Czech)
Výuka: přednáška, klasické cvičení. Zkouška písemná a ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2004, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2004/M4122