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    Reg. No. CZ.1.07/2.2.00/28.0326
    Subject: Probability and Statistics
    Form of study: full-time
    Subjetc´s goals: The course is focused on the probabilistic theory including mathematical basis for the description of discrete and continuous probability models. Students will be acquainted with the processing of one-dimensional statistical data, the theory of point and interval estimation and statistical tests that are based on normal probability distribution. The practical implementation of exploratory data analysis, calculation of estimates and statistical characteristics including the statistical hypothesis testing will be done using the software environment STAT1 and R. Statistical data and illustrative examples will be chosen with an emphasis on the field of study.
    Learning outcomes:
    • skills:
    • application of the basic methods of descriptive and inductive statistics
    • usage of methods of collecting real data and creation of data files for statistical analysis
    • abilities:
    • identification of the basic statistical methods
    • collecting data and their interpretation
    • competences:
    • active use and interpretation of the results of the learned methods
    Subject continuity: The course builds on the courses of Mathematics and Computer science.
    Conditions for successful completion of the course:
    • processing, presentation and defence of the seminar paper
    • written and oral examination corresponding to the content of the subject
    Basic literature:
    • Mann, Prem S. Introductory Statistics. Wiley, 2007, ISBN 978-0-471-75530-2.
    • Curl, James C., Mann, Prem S. Introductory Statistics, Student Study Guide. Wiley, 2007, ISBN 978-0-471-75532-6.
    • Johnson, Richard A., Bhattacharyya, Gouri K. Statistics: Principles and Methods. Wiley, 2006. ISBN 978-0-471-65682-1.
    • Olofsson, Peter Probability, Statistics, and Stochastic Processes. Wiley, 2005, ISBN 978-0-471-67969-1.
    Recommended readings:

  • Téma 1

    • Series and integrals Soubor
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      Introduction to series and integral calculus

  • Téma 2

    • Descriptive statistics Soubor
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      Organizing and displaying data, computing basic characteristics

  • Téma 3

    • Probability Soubor
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      Definition of probability, geometric and conditional probability

  • Téma 4

    • Random variables Soubor
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      Random variables and their characteristics, models of discrete and continuous random variables

  • Téma 5

    • Large numbers and samples Soubor
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      Law of large numbers, limit theorems and distribution of large samples

  • Téma 6

    • Point and interval estimators Soubor
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      Point and interval estimates of a parameter and distribution

  • Téma 7

    • Hypothesis testing Soubor
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      Tests of hypothesis about parameters and distributions

  • Téma 8

    • Correlation Soubor
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      Correlation analysis and correlation coefficients

  • Téma 9

    • Statistical linkage Soubor
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      Contingency tables and sample survey

  • Téma 10

    • Software Soubor
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      Examples in sthe tatistical software Stat1 (Excel application) and R