470-2405/01 – Probability (PRA)
| Gurantor department | Department of Applied Mathematics | Credits | 7 |
| Subject guarantor | Ing. Jan Kracík, Ph.D. | Subject version guarantor | Ing. Jan Kracík, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 2 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FEI | Intended for study types | Bachelor |
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:
Recommended literature:
Additional study materials
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction