Mathematical Statistics

Kód předmětu: 101MTST
Garant předmětu: RNDr. Martin Hála, CSc.
Zakončení předmětu: Z,ZK
Počet kreditů: 3 kred.
Rozsah výuky: 2+1

Anotace(semestr )
Advanced methods of mathematical statistics, notions of probability, discrete and continuous random variables, multidimensional distributions and estimates of distribution parameters. Multidimensional regression and submodel testing. Different types of continuous distributions. Multidimensional distribution. Time series, especially stationary time series and their study in time and frequency domain.
Obsah 
Notion of probability.
Discrete random variables.
Continuous random variables.
Types of continuous distributions.
Continuous random vectors.
Multidimensional distributions. in particular multivariate normal distribution.
Estimates of distribution parameters.
Notion of hypothesIs testing.
Specific hypotheses tests.
Linear regression.
Multidimensional regression.
Submodel testing.
Time series, in particular stationary time series and their study in time and frequency domain.
Literatura 
Povinná literatura:
[1]  Wasserman L.: All of Statistics. Springer, 2005. ISBN 0-387-40272-1
[2]  Papoulis, A. - Pillai, S.U.: Probability, Random Variables and Stochastic Processes. McGraw-Hill Europe; 4th edition, 2002. ISBN 0-07-366011-6
[3]  Hothorn, T. – Everitt, B. S.: Chapman & Hall/CRC Press, Boca Raton, Florida, USA, 3rd edition, 2014. ISBN 978-1-4822-0458-2.
[4]  Stowell, S.: Using R for Statistics. Springer, Berlin, 2014. ISBN 978-1484201404.
Návaznosti 
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Studijní plány 
Předmět je zařazen do následujících studijních plánů:

- studijní plán Civil Engineering (ND2023), skupina Civil Engineering, 1st semester (ND20230100), dop. semestr 1 (valid starting in 2023/24 )
- studijní plán Civil Engineering (ND2024), skupina Civil Engineering, 1st semester (ND20230100), dop. semestr 1 (valid from 2024/25 )