230-0203/02 – Mathematics III (BcM III)
| Gurantor department | Department of Mathematics | Credits | 5 |
| Subject guarantor | RNDr. Radomír Paláček, Ph.D. | Subject version guarantor | RNDr. Radomír Paláček, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 2 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2018/2019 | Year of cancellation | |
| Intended for the faculties | FAST | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
The aim of the course is to provide theoretical and practical foundation for understanding of the meaning of basic
probability terms and teach the student to statistical thinking as a way of understanding of the processes and
events around us, to acquaint him with the basic methods of statistical data gathering and analyzing, and to show
how to use these general procedures in other subjects of study and in practice.
Graduates of this course should be able to:
• understand and use the basic terms of combinatorics and probability theory;
• formulate questions that can be answered by the data, learn the principles of data collecting, processing and
presenting;
• select and use appropriate statistical methods for data analysis;
• propose and evaluate conclusions (inferences) and predictions using the data.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
Combinatorics and probability. Random events, operations with them, sample space.
Definitions of events' probability - classical, geometrical, statistics. Conditional probability. Total probability
and independent events.
Random variable and its characteristics.
Basic types of probability distributions of discrete random variables.
Basic types of probability distributions of continuous random variables.
Random vector, probability distribution, numerical characteristics.
Statistical file with one factor. Grouped frequency distribution.
Statistical file with two factors.
Regression and correlation.
Random sample, point and interval estimations of parameters.
Hypothesis testing.iables: two-dimensional integrals, three-dimensional integrals,
line integral of the first and the second kind.
Probabilities of random events: axioms of probability,
conditional probability, independence. Random variables: discrete random
variables, continuous random variables, expected values. Important practical
distributions of discrete and continuous random variables.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Passing the course, requirements
Course-credit
-participation on tutorials is obligatory,
-elaborate programs,
Point classification: 5-20 points.
Exam
Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least
25 points.
Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student obtains
at least 5 points.
Point quantification in the interval 100 - 86 85 - 66 65 - 51 50 - 0
National grading scheme excellent very good satisfactory failed
1 2 3 4
List of theoretical questions:
1. Combinatorics.
2. Random events.
3. Probabilities of random events - clasical, geometrical, statistical.
4. Conditional probability.
5. Composite probability.
6. Bernoulli sequence of independent random trials.
7. Bayes formula.
8. Discrete random variable.
9. Continuous random variable.
10. Probability mass and density function. Probability distribution funciton.
11. Characteristics of random variables.
12. Basic types of probability distributions of discrete random variables.
13. Basic types of probability distributions of continuous random variables.
14. Random vectors, their probabilities distribution and characteristics.
15. Processing of the statistical sample.
16. Random selection.
17. Point estimates.
18. Interval estimates.
19. Testing of hypothesis, parametrical tests.
20. Testing of hypothesis, nonparametrical tests.
21. Linear regression.
22. Least square method.
E-learning
http://www.studopory.vsb.cz
http://mdg.vsb.cz
(in Czech language)
Other requirements
At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Syllabus of lecture
Combinatorics. Random events and their operations.
Probabilities of random events - clasical, geometrical, statistical. Conditional probability. Composite probability.
Bernoulli sequence of independent random trials. Bayes formula.
Discrete and continuous random variable. Probability mass and density function. Probability distribution funciton.
Characteristics of random variables.
Basic types of probability distributions of discrete and continuous random variables.
Random vectors, their probabilities distribution and characteristics.
Processing of the statistical sample.
Random selection, point and interval estimates.
Testing of hypothesis - parametrical and nonparametrical tests.
Linear regression. Least square method.
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction