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Lecturer(s)
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Urbánek Tomáš, Ing. Ph.D.
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Zimola Bedřich, RNDr. Ph.D.
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Course content
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<h5><b><u>First Part of the Semester</u></b></h5> <ul> <li>Basic Concepts</li> <li>Data and Descriptive Statistics of Central Tendency <ul> <li>Types of data</li> <li>Mean</li> <li>Median</li> </ul> </li> <li>Descriptive Statistics of Variance and Shape <ul> <li>Variance</li> <li>Skewness</li> <li>Kurtosis</li> </ul> </li> <li>Probability <ul> <li>Axioms of probability</li> <li>Definition of probability</li> </ul> </li> <li>Conditional Probability and Bayes' Theorem <ul> <li>Total probability</li> <li>Conditional probability</li> <li>Bayes' theorem</li> </ul> </li> </ul> <h5><b><u>Second Part of the Semester</u></b></h5> <ul> <li>Random Variable 1 <ul> <li>Probability function</li> <li>Probability density function</li> <li>Cumulative distribution function</li> </ul> </li> <li>Random Variable 2 <ul> <li>Quantile function</li> <li>Reliability function</li> <li>Hazard function</li> </ul> </li> <li>Distribution of Discrete Random Variable <ul> <li>Uniform distribution</li> <li>Geometric distribution</li> <li>Hypergeometric distribution</li> <li>Binomial distribution</li> <li>Poisson distribution</li> </ul> </li> <li>Distribution of Continuous Random Variable 1 <ul> <li>Uniform continuous distribution</li> <li>Normal distribution</li> <li>Exponential distribution</li> <li>Weibull distribution</li> </ul> </li> <li>Distribution of Continuous Random Variable 2 <ul> <li>Student's distribution</li> <li>Chi-square distribution</li> <li>F-distribution</li> </ul> </li> </ul>
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Learning activities and teaching methods
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Lecturing
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| prerequisite |
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| Knowledge |
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| Knowledge of basic higher mathematics (the investigation of functions, derivatives and integrals). |
| Knowledge of basic higher mathematics (the investigation of functions, derivatives and integrals). |
| learning outcomes |
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| Defines concepts associated with data and descriptive statistics of location |
| Defines concepts associated with data and descriptive statistics of location |
| Describes statistics such as variance, skewness, and kurtosis, which characterize dispersion and the shape of distributions |
| Describes statistics such as variance, skewness, and kurtosis, which characterize dispersion and the shape of distributions |
| Explains fundamental probability concepts |
| Explains fundamental probability concepts |
| Explains concepts associated with random variables |
| Explains concepts associated with random variables |
| Lists and defines various distributions of discrete random variables |
| Lists and defines various distributions of discrete random variables |
| Lists and defines various distributions of continuous random variables |
| Lists and defines various distributions of continuous random variables |
| Skills |
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| Addresses practical tasks that involve the application of probability and descriptive statistics |
| Addresses practical tasks that involve the application of probability and descriptive statistics |
| Uses probability functions for different types of random variables |
| Uses probability functions for different types of random variables |
| Applies distribution functions for random variables based on provided information |
| Applies distribution functions for random variables based on provided information |
| Conducts the analysis of random variables |
| Conducts the analysis of random variables |
| Resolves issues related to diverse distributions of random variables and interprets their meaning |
| Resolves issues related to diverse distributions of random variables and interprets their meaning |
| teaching methods |
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| Knowledge |
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| Lecturing |
| Lecturing |
| assessment methods |
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| Grade (Using a grade system) |
| Grade (Using a grade system) |
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Recommended literature
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Clarke, G. M., Cooke, D. A basic course in statistics. 2nd ed. London: Edward Arnold,, 1983. ISBN 0-7131-3496-8.
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Hogg, R.V., Craig, A.T. Introduction to mathematical statistics. 4th ed. New York: Macmillan Publishing Company, 1989.
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Kropáč, Jiří. Základy teorie pravděpodobnosti a matematické statistiky. Zlín : UTB, 2003. ISBN 80-7318-139-8.
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Likeš, Jiří, Machek, Josef. Matematická statistika - Matematika pro vysoké školy technické, sešit XI. Praha : SNTL, 1983.
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Lloyd, E. H. Handbook of applicable mathematics 2 : probability. Chicester Wiley, 1980. ISBN 0-471-27821-1.
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Swoboda, Helmut. Moderní statistika. Vyd. 1. Praha : Svoboda, 1977.
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