Course objectives:
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The aim of this course is to introduce basic ideas and methods of probability and statistical analysis.
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Requirements on student
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Students have to achieve at least 60% of points in two written test (8-th & 13-th week of term). Every test consists of 4 examples similar to examples solved in previous lectures and tutorials.
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Content
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1. Random event. Probability and its properties.
2. Independence of events. Conditional probability. The theorem of total probability.
3. Random variable, distribution function. Expectatation and dispersion.
4. Discrete random variables. Hypergeometric, binomial and Poisson distributions.
5. Continuous random variables, probability density function. Uniform, exponential and Weibull and normal distributions.
6. Approximation by a normal distribution. Quantiles of a continuous random variable, median.
7. A random multivariate distribution, covariance, correlation coefficient. Multivariate normal distribution.
8. Random sample. Collection of statistical data, descriptive statistics.
9. Point estimation, interval estimation of parameters.
10. Statistical hypothesis, critical region, significance level, type I and type II error Testing the mean of a normal distribution, comparing the mean and variances of two normal distributions. 11. Goodness-of-fit tests. Chi-square test, contingency tables. Sample correlation coefficient and its properties. Tests of independence.
12. Regression function, simple and multiple linear regression. Coefficient of determination. 13. Statistical methods of quality assurance - example. Final remarks.
If you need more information see http://www.kma.zcu.cz/PSB , please
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for comprehensive test (10-40)
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39
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Contact hours
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39
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Total
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78
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
formulovat základní kombinatorické úlohy pomocí kombinatorických vzorců ( v rozsahu běžném na SŠ ) |
charakterizovat základní techniky pro výpočet derivace a integrálu funkce jedné proměnné (v rozsahu M1S) |
popsat vlastnosti elementárních funkcí reálné proměnné |
využít geometrickou interpretaci derivace při hledání průběhu a extrémů funkce |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
zvládat základní operace s faktoriály a kombinačními čísly |
vypočítat obsah množiny použitím určitého integrálu |
provádět běžné numerické výpočty derivací a integrálu |
načrtnout grafy elementárních funkcí s vyznačením důležitých bodů |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
popsat náhodné jevy a spočítat jejich pravděpodobnost |
rozpoznat a použít základní typy diskrétních a spojitých rozdělení pravděpodobnosti |
použít metody popisné statistiky k shrnutí informací z dat |
formulovat statistickou hypotézu a vybrat vhodný statistický test k jejímu přijetí nebo zamítnutí |
interpretovat statistické výsledky |
Skills - skills resulting from the course: |
vypočítat bodové odhady a sestrojit intervaly spolehlivosti |
vypracovat postup a navrhnout rozsah výběru při statistické kontrole jakosti |
zpracovat data použitím matod korelační a regresní analýzy |
rozhodnout na základě výsledků testu o přijetí či zamítnutí statistické hypotézy |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Test |
Skills demonstration during practicum |
Skills - skills achieved by taking this course are verified by the following means: |
Test |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Test |
Skills demonstration during practicum |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Skills - the following training methods are used to achieve the required skills: |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Textual studies |
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