Czech

5

Not applicable.

Acquired knowledge can be applied, for example, in other courses or in the BSc/MSc thesis.

Secondary school mathematics and selected topics from previous mathematical courses.

Not applicable.

Not applicable.

1. 1. Introduction to probability theory. Combinatorics and classical probability.
   2. Axiomatic probability. Conditional probability and independence. Probability rules. Total probability, Bayes' theorem.
   3. Random variable (discrete and continuous), probability mass function, cumulative distribution function, probability density function. Characteristics of random variables (mean, variance, skewness, kurtosis).
   4. Discrete probability distributions: Bernoulli, binomial, hypergeometric, geometric, Poisson.
   5. Continuous probability distributions: uniform, exponencial,  normal. Central limit theorem.
   6. Basic arithmetics with random variables and their influence on the parameters of probability distributions.
   7. Random vector (discrete and continuous). Joint and marginal probability mass function, cumulative distribution function, probability density function. Characteristics of random vectors (mean, variance, covariance, correlation coefficient). Independence. Multivariate normal distribution.
   8. Introduction to statistics. Descriptive statistics. Data processing. Characteristics of central tendency, variability and shape. Moments. Graphical representation of the data.
   9. Estimation theory. Point estimates. Maximum likelihood method.
   10. Interval estimates. Statistical hypothesis testing. One-sample and two-sample tests (t-test,  F-test).
   11. Goodness-of-fit tests.
   12. Introduction to regression analysis. Linear regression.
   13. Correlation analysies. Pearson's and Spearman's correlation coefficient.

 

Not applicable.

The main goal of the course is to introduce basic principles and methods of probability and mathematical statistics which are useful not only in computer sciences.

Class attendance. If students are absent due to medical reasons, they should contact their lecturer.

Not applicable.

Not applicable.

Fajmon, B., Hlavičková, I., Novák, M., Vítovec, J.: Numerická matematika a pravděpodobnost (Informační technologie), VUT v Brně, 2016 (CS)
Hlavičková, I., Hliněná, D.: Matematika 3. Sbírka úloh z pravděpodobnosti. VUT v Brně, 2015 (CS)
Anděl, J.: Matematická statistika. Praha: SNTL, 1978. (CS)
Fajmon, B., Hlavičková, I., Novák, M., Vítovec, J.: Numerická matematika a pravděpodobnost (Informační technologie), VUT v Brně, 2016 (CS)
Anděl, J.: Statistické metody. Praha: Matfyzpress, 1993. (CS)
Hlavičková, I., Hliněná, D.: Matematika 3. Sbírka úloh z pravděpodobnosti. VUT v Brně, 2015 (CS)
Anděl, J.: Základy matematické statistiky. Praha: Matfyzpress, 2005. (CS)
Casella, G., Berger, R. L.: Statistical Inference. Pacific Grove, CA: Duxbury Press, 2001. (EN)
Hogg, R. V., McKean, J., Craig, A. T.: Introduction to Mathematical Statistics. Boston: Pearson Education, 2013. (EN)
Likeš, J., Machek, J.: Matematická statistika. Praha: SNTL - Nakladatelství technické literatury, 1988. (CS)
Likeš, J., Machek, J.: Počet pravděpodobnosti. Praha: SNTL - Nakladatelství technické literatury, 1987. (CS)
Montgomery, D. C., Runger, G. C.: Applied Statistics and Probability for Engineers. New York: John Wiley & Sons, 2011. (EN)
Neubauer, J., Sedlačík, M., Kříž, O.: Základy statistiky. Praha: Grada Publishing, 2012. (CS)
Montgomery, D. C., Runger, G. C.: Applied Statistics and Probability for Engineers. New York: John Wiley & Sons, 2011. (EN)

26 hours, compulsory