470-2405/01 – Probability (PRA)

Gurantor departmentDepartment of Applied MathematicsCredits7
Subject guarantorIng. Jan Kracík, Ph.D.Subject version guarantorIng. Jan Kracík, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semesterwinter
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRA0220 Ing. Jan Kracík, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2
Part-time Credit and Examination 12+8

Subject aims expressed by acquired skills and competences

Students will understand basic concepts and relations in probability theory needed for mathematical statistics.

Teaching methods

Lectures
Tutorials
Project work

Summary

Probability theory provides a framework for treating uncertainty and is a foundation for mathematical statistics. Students will gain knowledge of fundamental notions of probability theory at a level not requiring knowledge of measure theory.

Compulsory literature:

RAO, C. RADHAKRISHNA. Linear statistical inference and its applications. 2. ed., paperback ed. New York: Wiley, 2002. ISBN 0471218758.

Recommended literature:

TEETOR, Paul. R cookbook. Sebastopol, CA: O'Reilly, 2011. ISBN 9780596809157

Way of continuous check of knowledge in the course of semester

2 tests per during the semester semestral project

E-learning

Other requirements

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Probability space Conditional probability, independent random events, law of total probability, Bayes' theorem Conditional independence of random events Random variable, probability distribution, numerical characteristics Selected discrete distributions Selected continuous distributions Multivariate random variable, probability distribution, numerical characteristics Independece of random variables, conditional independence Multivariate normal distribution Convergence of random variables Limit theorems Transformations of random variables, sum of random variables, sampling Excercises will follow the content of the lectures. During the excercises students will learn basics of R language.

Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  35
Mandatory attendence parzicipation: Obligatory participation at all excercises, 2 apologies are accepted

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (B0541A170008) Computational and Applied Mathematics VMI P Czech Ostrava 2 Compulsory study plan
2020/2021 (B0541A170008) Computational and Applied Mathematics VMI K Czech Ostrava 2 Compulsory study plan
2019/2020 (B0541A170008) Computational and Applied Mathematics VMI P Czech Ostrava 2 Compulsory study plan
2019/2020 (B0541A170008) Computational and Applied Mathematics VMI K Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner