| Course Unit Code | 230-0303/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Choice-compulsory type B |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | Second Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| BOH10 | doc. RNDr. Zdeněk Boháč, CSc. |
| KRE40 | doc. RNDr. Pavel Kreml, CSc. |
| JAR71 | Mgr. Marcela Jarošová, Ph.D. |
| POS220 | Ing. Lukáš Pospíšil, Ph.D. |
| SVE0150 | Ing. Veronika Moškořová, Ph.D. |
| Summary |
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Random variables: Discrete and continuous random variables, probability distribution, density function, mean, variance, standard deviation. Characteristics of population and sample, measures of central tendency, measures of dispersion sampling distributions. Point estimates, confidence interval, testing hypotheses.
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| Learning Outcomes of the Course Unit |
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The goal of the course is to serve as a theoretical and practical base to understand the importance of the basic notions in probability, and teach the student statistical way of thinking as a mean of understanding real life processes, introduce basic methods of collecting and analysing statistical data, and show the student how to use these general methods in other courses of study and in professional career.
The graduate of this course should be able:
• understand and use basic notions in combinatorics and probability theory
• formulate questions, which can be answered based on the given data, for this purpose learn the principles of collecting, processing data and presentation of relevant values and results
• choose and use suitable statistical methods for data analysis
• suggest and evaluate conclusions (inference) and predictions obtained from data
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| Course Contents |
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1. Random event, experiment, definition of probability. Conditional probability, independent events and its probability.
2. Random variable. Discrete random variable, probability function, distribution function of a discrete random variable. Numerical characteristics. Discrete uniform distribution, Poisson distribution, binomial distribution, hypergeometric distribution.
3. Continuous random variable. Probability density function, distribution function of a continuous random variable, numerical characteristics. Uniform distribution, exponential distribution, normal distribution.
4. Population. Data sample, frequency distributions.
5. Random sample and empirical characteristics.
6. Point and interval estimates of parameters, method of moments and maximum likelihood method.
7. Correlation and regression analysis, covariant and correlation matrix.
8. Approximation by the method of least squares.
9. Tests of hypotheses.
10. F-test of the equality of two variances.
11. Unpaired and paired two-sample t-tests.
12. Pearson's test, Kolmogorov–Smirnov test, two-sample Kolmogorov–Smirnov test.
13. Dixon's Q test, Grubbs' test for outliers.
14. Reserve. |
| Recommended or Required Reading |
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| Required Reading: |
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[1] Triola, Mario, F.: Elementary Statistics. Benjamin/Cummings Publ. Comp.,
Inc., Redwood City, California 1989.
[2] Boháč, Z.: Numerical Methods and Statistics. VŠB – TUO, Ostrava 2005.
ISBN 80-248-0803-X
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[1] Pavelka,L.,Doležalová,J.: Pravděpodobnost a statistika. Skriptum VŠB,
Ostrava 1999. ISBN 80-7078-976-X
[2] Hebák,P., Hustopecký,J.: Vícerozměrné statistické metody s aplikacemi.
SNTL, Alfa, Praha 1990. ISBN 80-03-00534-5
[3] http://homen.vsb.cz/~oti73/cdpast1/
[4] Boháč, Z.: Numerical Methods and Statistics. VŠB – TUO, Ostrava 2005.
ISBN 80-248-0803-X
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| Recommended Reading: |
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[1] Buchanan, James., L.,Turner, Peter., R.: Numerical Methods and Analysis.
McGraw-Hill, Inc. New York 1992. ISBN 0-07-008717-2
[2] https://homel.vsb.cz/~bri10/Teaching/Prob%20&%20Stat.pdf |
[1] Boháč, Z., Častová,N.: Základní numerické metody. Skriptum VŠB-TUO,
Ostrava 1997. ISBN 80-7078-975-1
[2] Buchanan, James., L.,Turner, Peter., R.: Numerical Methods and Analysis.
McGraw-Hill, Inc. New York 1992. ISBN 0-07-008717-2 |
| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials, Other activities |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 20 | 10 |
| Examination | Examination | 80 (80) | 30 |
| Písemná zkouška | Written examination | 60 | 25 |
| Ústní zkouška | Oral examination | 20 | 5 |