PřF:M4122 Probability and Statistics II - Course Information
M4122 Probability and Statistics II
Faculty of ScienceSpring 2025
- 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)
Mgr. Jan Ševčík (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 - 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
- Applied Mathematics for Multi-Branches Study (programme PřF, B-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematical Biology (programme PřF, B-EXB)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- 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
- Characteristics: covariance, moments and their properties, covariance and correlation matrices, characteristic function of random vector. Limit theorems: Borel and Cantelli theorem, Cebyshev's inequality, Laws of large numbers, central limit theorem. 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.
The course is taught: every week. - Listed among pre-requisites of other courses
- Enrolment Statistics (Spring 2025, recent)
- Permalink: https://is.muni.cz/course/sci/spring2025/M4122