M4122 Probability and Statistics II

Faculty of Science
Spring 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).
In-person direct teaching
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
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, probability generating function, moment generating function. 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. A Monte Carlo simulation concept, permutation methods and bootstrap 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.
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
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 2021, Spring 2022, Spring 2023, Spring 2024.

M4122 Probability and Statistics II

Faculty of Science
Spring 2024
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
Timetable
Mon 19. 2. to Sun 26. 5. Mon 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Mon 19. 2. to Sun 26. 5. Thu 10:00–11:50 M1,01017, J. Koláček
M4122/02: Mon 19. 2. to Sun 26. 5. Mon 16:00–17:50 M6,01011, J. Ševčík
M4122/03: Mon 19. 2. to Sun 26. 5. Mon 14:00–15:50 M6,01011, J. Ševčík
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
  • 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)
Study Materials
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 2021, Spring 2022, Spring 2023, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
Spring 2023
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
Timetable
Thu 14:00–15:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Wed 14:00–15:50 M2,01021, J. Koláček
M4122/02: Tue 10:00–11:50 M2,01021, J. Ševčík
M4122/03: Mon 16:00–17:50 M6,01011, J. Ševčík
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
  • 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)
Study Materials
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 2021, Spring 2022, Spring 2024, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
Spring 2022
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
Timetable
Thu 16:00–17:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Thu 10:00–11:50 M1,01017, J. Koláček
M4122/02: Mon 8:00–9:50 M1,01017, J. Ševčík
M4122/03: Thu 8:00–9:50 M4,01024, J. Ševčík
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
  • 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)
Study Materials
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 2021, Spring 2023, Spring 2024, Spring 2025.

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.

M4122 Probability and Statistics II

Faculty of Science
Spring 2020
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. Radim Navrátil, Ph.D. (seminar tutor)
Mgr. Ondřej Pokora, 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
Thu 8:00–9:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Wed 10:00–11:50 M1,01017, R. Navrátil
M4122/02: Thu 16:00–17:50 M4,01024, O. Pokora
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)
Study Materials
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 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
Spring 2019
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. Radim Navrátil, 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 18. 2. to Fri 17. 5. Wed 8:00–9:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Mon 18. 2. to Fri 17. 5. Wed 14:00–15:50 M2,01021, J. Koláček
M4122/02: Mon 18. 2. to Fri 17. 5. Wed 10:00–11:50 M1,01017, R. Navrátil
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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)
Study Materials
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 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
spring 2018
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. Radim Navrátil, 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 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Mon 10:00–11:50 M1,01017, J. Koláček
M4122/02: Wed 10:00–11:50 M4,01024, R. Navrátil
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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)
Study Materials
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 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
Spring 2017
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. Radim Navrátil, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 20. 2. to Mon 22. 5. Mon 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Mon 20. 2. to Mon 22. 5. Tue 10:00–11:50 M2,01021, R. Navrátil
M4122/02: Mon 20. 2. to Mon 22. 5. Thu 12:00–13:50 M3,01023, R. Navrátil
M4122/03: Mon 20. 2. to Mon 22. 5. Mon 10:00–11:50 M2,01021, J. Koláček
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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)
Study Materials
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 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
Spring 2016
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. Radim Navrátil, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Wed 10:00–11:50 M1,01017, J. Koláček
M4122/02: Thu 16:00–17:50 M1,01017, R. Navrátil
M4122/03: Mon 10:00–11:50 M3,01023, R. Navrátil
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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 8 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)
Study Materials
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 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
Spring 2015
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. Radim Navrátil, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Wed 15:00–16:50 M2,01021, J. Koláček
M4122/02: Thu 18:00–19:50 M1,01017, R. Navrátil
M4122/03: Wed 16:00–17:50 M1,01017, R. Navrátil
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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 8 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)
Study Materials
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 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
Spring 2014
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. Dagmar Lajdová (seminar tutor)
Mgr. Ondřej Pokora, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 10:00–11:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Mon 12:00–13:50 M2,01021, O. Pokora
M4122/02: Wed 14:00–15:50 M5,01013, O. Pokora
M4122/03: Tue 16:00–17:50 M1,01017, D. Lajdová
M4122/04: Tue 18:00–19:50 M1,01017, D. Lajdová
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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 8 theoretical questions, each for 10 points. The final result is corrected by the oral part. Final grade: A: 72 - 80 points B: 63 - 71 points C: 54 - 62 points D: 45 - 53 points E: 36 - 44 points F: 0 - 35 points
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
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 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
Spring 2013
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. Dagmar Lajdová (seminar tutor)
Mgr. Ondřej Pokora, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 14:00–15:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Tue 12:00–13:50 M2,01021, J. Koláček
M4122/02: Tue 16:00–17:50 M2,01021, D. Lajdová
M4122/03: Tue 18:00–19:50 M2,01021, D. Lajdová
M4122/04: Mon 12:00–13:50 M2,01021, O. Pokora
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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, 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 basic concepts, solving theoretical problems, solving simpler tasks and also complicated problems, homeworks
Assessment methods
Lectures and exercises. Active work in exercises. Two written tests within the semester. Examination consists of two parts: written and oral.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
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 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
Spring 2012
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. Jakub Čupera, Ph.D. (seminar tutor)
Mgr. Lenka Zavadilová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 14:00–15:50 A,01026
  • Timetable of Seminar Groups:
M4122/01: Fri 10:00–11:50 M4,01024, L. Zavadilová
M4122/02: Wed 16:00–17:50 M5,01013, J. Čupera
M4122/03: Thu 12:00–13:50 M2,01021, L. Zavadilová
M4122/04: Wed 18:00–19:50 M5,01013, J. Čupera
M4122/05: Wed 16:00–17:50 M4,01024, J. Koláček
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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, 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 basic concepts, solving theoretical problems, solving simpler tasks and also complicated problems, homeworks
Assessment methods
Lectures and exercises. Active work in exercises. Two written tests within the semester. Examination consists of two parts: written and oral.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
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 - 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.

M4122 Probability and Statistics II

Faculty of Science
Spring 2011
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)
RNDr. Marie Forbelská, Ph.D. (lecturer)
Mgr. Jakub Čupera, Ph.D. (seminar tutor)
Mgr. Lenka Zavadilová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 12:00–13:50 M1,01017
  • Timetable of Seminar Groups:
M4122/01: Thu 14:00–15:50 M2,01021, L. Zavadilová
M4122/02: Thu 16:00–17:50 M1,01017, L. Zavadilová
M4122/03: Thu 16:00–17:50 M2,01021, J. Čupera
M4122/04: Thu 12:00–13:50 M4,01024, J. Čupera
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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, 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 basic concepts, solving theoretical problems, solving simpler tasks and also complicated problems, homeworks
Assessment methods
Lectures and exercises. Active work in exercises. Two written tests within the semester. Examination consists of two parts: written and oral.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
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 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.

M4122 Probability and Statistics II

Faculty of Science
Spring 2010
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Gejza Wimmer, DrSc. (lecturer)
Mgr. Jakub Čupera, Ph.D. (seminar tutor)
Mgr. Lenka Zavadilová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 11:00–12:50 M1,01017
  • Timetable of Seminar Groups:
M4122/01: Wed 18:00–19:50 M5,01013, J. Čupera
M4122/02: Thu 18:00–19:50 M4,01024, L. Zavadilová
M4122/03: Wed 14:00–15:50 M4,01024, L. Zavadilová
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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, 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 basic concepts, solving theoretical problems, solving simpler tasks and also complicated problems, homeworks
Assessment methods
Lectures and exercises. Active work in exercises. Two written tests within the semester. Examination consists of two parts: written and oral.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
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 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.

M4122 Probability and Statistics II

Faculty of Science
Spring 2009
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Forbelská, Ph.D. (lecturer)
doc. Mgr. Kamila Hasilová, Ph.D. (seminar tutor)
Mgr. Jitka Kühnová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 13:00–14:50 M1,01017
  • Timetable of Seminar Groups:
M4122/01: Wed 10:00–11:50 M2,01021, J. Kühnová
M4122/02: Thu 18:00–19:50 M5,01013, K. Hasilová
M4122/03: Wed 12:00–13:50 M2,01021, J. Kühnová
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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, 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.
Assessment methods
Lecture with a seminar. Active work in seminars. Examination consists of two parts: written and oral.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
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 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.

M4122 Probability and Statistics II

Faculty of Science
Spring 2008
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Gejza Wimmer, DrSc. (lecturer)
Mgr. Pavla Krajíčková, Ph.D. (seminar tutor)
RNDr. Tomáš Pavlík, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 12:00–13:50 N21
  • Timetable of Seminar Groups:
M4122/01: Thu 18:00–19:50 UP2, P. Krajíčková
M4122/02: Wed 18:00–19:50 UP2, T. Pavlík
M4122/03: Fri 12:00–13:50 UP2, T. Pavlík
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.
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, 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.
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)
Study Materials
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 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.

M4122 Probability and Statistics II

Faculty of Science
Spring 2007
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Forbelská, Ph.D. (lecturer)
doc. Mgr. Kamila Hasilová, Ph.D. (seminar tutor)
RNDr. Tomáš Pavlík, Ph.D. (seminar tutor)
Mgr. Jaroslava Sidorová (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
Fri 12:00–13:50 N21
  • Timetable of Seminar Groups:
M4122/01: Wed 17:00–18:50 N21, J. Sidorová
M4122/02: Mon 14:00–15:50 UP2, K. Hasilová
M4122/03: Mon 12:00–13:50 UP2, T. Pavlík
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.
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 2004, Spring 2005, Spring 2006, 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.

M4122 Probability and Statistics II

Faculty of Science
Spring 2006
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)
doc. Mgr. Jan Koláček, 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
Thu 15:00–16:50 N21
  • Timetable of Seminar Groups:
M4122/01: Tue 11:00–12:50 M3,04005 - dříve Janáčkovo nám. 2a, Tue 11:00–12:50 N41
M4122/02: Mon 18:00–19:50 M3,04005 - dříve Janáčkovo nám. 2a, Mon 18:00–19:50 N21
M4122/03: Mon 16:00–17:50 M3,04005 - dříve Janáčkovo nám. 2a, Mon 16:00–17:50 N21
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 2004, Spring 2005, 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.

M4122 Probability and Statistics II

Faculty of Science
Spring 2005
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)
RNDr. Štěpán Mikoláš (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
Thu 14:00–15:50 N21
  • Timetable of Seminar Groups:
M4122/01: Mon 8:00–9:50 UP1, M. Forbelská, Rozvrhově doporučeno: M,Mo
M4122/02: Thu 18:00–19:50 N21, Š. Mikoláš, Rozvrhově dopdoručeno: Mb,Mf,Ms
M4122/03: Tue 17:00–18:50 N21, Š. Mikoláš, Rozvrhově dopdoručeno: Me
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
there are 9 fields of study the course is directly associated with, display
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 2004, 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.

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.

M4122 Probability and Statistics II

Faculty of Science
Spring 2003
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jaroslav Michálek, CSc. (lecturer)
doc. Mgr. Zuzana Hübnerová, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jaroslav Michálek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Jaroslav Michálek, CSc.
Timetable of Seminar Groups
M4122/01: No timetable has been entered into IS. Z. Hübnerová
M4122/02: No timetable has been entered into IS. Z. Hübnerová
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 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 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

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)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
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
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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, 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 basic concepts, solving theoretical problems, solving simpler tasks and also complicated problems, homeworks
Assessment methods
Lectures and exercises. Active work in exercises. Two written tests within the semester. Examination consists of two parts: written and oral.
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
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 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.

M4122 Probability and Statistics II

Faculty of Science
Spring 2011 - only for the accreditation
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)
RNDr. Marie Forbelská, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Gejza Wimmer, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
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. As a result of successfully completing this course, students will have demonstrated an acceptable level of mastery of the concepts and applications of an introductory course in statistics.
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, 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 basic concepts, solving theoretical problems, solving simpler tasks and also complicated problems, homeworks
Assessment methods
Lectures and exercises. Active work in exercises. Two written tests within the semester. Examination consists of two parts: written and oral.
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
The course is also listed under the following terms Spring 2008 - for the purpose of 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 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M4122 Probability and Statistics II

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Forbelská, Ph.D. (lecturer)
prof. RNDr. Gejza Wimmer, DrSc. (lecturer)
doc. Mgr. Kamila Hasilová, Ph.D. (seminar tutor)
RNDr. Tomáš Pavlík, Ph.D. (seminar tutor)
Mgr. Jaroslava Sidorová (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.
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.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms 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 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (recent)