Statistics and Probability

• 26 hrs lectures
• 21 hrs exercises
• 5 hrs projects

• 70 pts final exam (written part)
• 20 pts mid-term test (written part)
• 10 pts projects

Students will extend their knowledge of probability and statistics, especially in the following areas:

• Parameter estimates for a specific distribution
• simultaneous testing of multiple parameters
• hypothesis testing on distributions
• regression analysis including regression modeling
• nonparametric methods
• Markov processes
• randomised algorithms 

Introduction of further concepts, methods and algorithms of probability theory, descriptive and mathematical statistics. Development of probability and statistical topics from previous courses. Formation of a stochastic way of thinking leading to formulation of mathematical models with emphasis on information fields.

The society development desires also technology and, in particular, information technology expansion. It is necessary to process information - data in order to control technology. Nowadays, there is a lot of devices that collect data automatically. So we have a large amount of data that needs to be processed. Statistical methods are one of the most important means of processing and sorting data, including their analysis. This allows us to obtain necessary information from your data to evaluate and control.

Foundations of differential and integral calculus.

Foundations of descriptive statistics, probability theory and mathematical statistics.

• Anděl, Jiří. Základy matematické statistiky. 3.,  Praha: Matfyzpress, 2011. ISBN 978-80-7378-001-2.
• FELLER, W.: An Introduction to Probability Theory and its Applications. J. Wiley, New York 1957. ISBN 99-00-00147-X
• Hogg, V.R., McKean J.W. and Craig A.T. Introduction to Mathematical Statistics. Seventh Edition, 2012. Macmillan Publishing Co., INC. New York. ISBN-13: 978-0321795434  2013
• Zvára, Karel. Regrese. 1., Praha: Matfyzpress, 2008. ISBN 978-80-7378-041-8
• Meloun M., Militký J.: Statistické zpracování experimentálních dat (nakladatelství PLUS, 1994).
• D. P. Bertsekas, J. N. Tsitsiklis. Introduction to Probability, Athena, 2008. Scientific

1. Summary of basic theory of probability and random variables: axiomatic definition of probability, conditional probability, discrete and continuous random variable, significant probability distributions, random vector.
2. Summary of basic methods in statistics: parameter estimate, hypothesis testing, goodness-of-fit tests, regression analysis - regression line.
3. Extension of hypothesis tests for binomial and normal distributions.
4. Analysis of variance (simple sorting, ANOVA), post hos analysis
5. Analysis of categorical data. Contingency table. Independence test. Four-field tables. Fisher's exact test.
6. Project assignment, demonstration of the use of statistical tools (programs) for solving the project and other statistical tasks.
7. Regression analysis. Creating a regression model. Testing hypotheses about regression model parameters. Comparison of regression models. Diagnostics.
8. Distribution tests.
9. Nonparametric methods of testing statistical hypotheses - part 1.
10. Nonparametric methods of testing statistical hypotheses - part 2.
11. Markov processes and their analysis. 
12. Markov decision processes and their basic analysis.
13. Introduction to randomized algorithms and their use (Monte Carlo, Las Vegas, applications).

1. Summary of basic theory of probability and random variables.
2. Summary of basic methods in statistics.
3. Hypothesis tests for binomial and normal distributions.
4. Analysis of variance, sorting, post host analysis.
5. Analysis of categorical data. Contingency table. Four-field tables.
6. Demonstration of the use of statistical tools (programs).
7. Regression analysis.
8. Tests on distribution, tests of good agreement.
9. Nonparametric methods of testing statistical hypotheses - one-sample.
10. Nonparametric methods of testing statistical hypotheses - two or more sample ones.
11. Application and analysis of Markov processes.
12. Basic application and analysis of Markov decision processes.
13. Design and analysis of basic randomised algorithms.  

1.  Usage of tools for solving statistical problems (data processing and interpretation).

Three tests will be written during the semester - 6th and 11th week. The exact term will be specified by the lecturer. The test duration is 60 minutes. The evaluation of each test is 0-10 points.

Projected evaluated 0-10 points.

Final written exam - 60 points

Participation in lectures in this subject is not controlled

Participation in the exercises is compulsory. During the semester two abstentions are tolerated. Replacement of missed lessons is determined by the leading exercises.

Fulfil the attendance conditions and achieve in total at least 15 points from the tests and the project.