M4122 Probability and Statistics II

Faculty of Science
Spring 2021
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Jan Koláček, Ph.D. (lecturer)
RNDr. Marie Budíková, Dr. (seminar tutor)
Mgr. Jakub Záthurecký, Ph.D. (seminar tutor)
Guaranteed by
doc. Mgr. Jan Koláček, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 1. 3. to Fri 14. 5. Mon 12:00–13:50 online_A
  • Timetable of Seminar Groups:
M4122/01: Mon 1. 3. to Fri 14. 5. Mon 10:00–11:50 online_M2, J. Koláček
M4122/02: Mon 1. 3. to Fri 14. 5. Wed 10:00–11:50 online_M2, M. Budíková
M4122/03: Mon 1. 3. to Fri 14. 5. Thu 18:00–19:50 online_M1, J. Záthurecký
Prerequisites
M3121 Probability and Statistics I
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.
Learning outcomes
As a result of successfully completing this course, a student is expected to obtain sufficient mastery of basic statistical inference theory; to apply central limit theorem in practical examples; to construct several types of point estimators and to know their statistical properties; to construct interval estimators; to test basic statistical hypothesis.
Syllabus
  • Random samples: definition and sample characteristics, unbiased and consistent estimators, samples from normal populations, examples of point and interval estimators. Theory of estimation: the best unbiased estimators, efficient estimators, methods for construction of point estimators (maximum likelihood method, moment method, quantiles and methods for interval estimation. Statistical hypotheses testing: basic concepts, Neyman-Pearson lemma, tests on parameters of normal distributions
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.
Teaching methods
Lectures: theoretical explanation with practical examples Exercises: solving problems for acquirement of basic concepts, solving theoretical problems, solving simpler tasks and also complicated problems
Assessment methods
Lectures and exercises. Active work in exercises. Two written tests within the semester. Each test consists of 4-5 examples and is for 20 points. 50% of points is needed to pass fulfilling requirements. Examination consists of two parts: written and oral. Written part consists of 4 theoretical questions, each for 10 points. The final result is corrected by the oral part. Final grade: A: 37 - 40 points B: 32 - 36 points C: 27 - 31 points D: 22 - 26 points E: 18 - 21 points F: 0 - 17 points
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 2004, 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 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2021, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2021/M4122