Probability and Statistics
Code  Completion  Credits  Range  Language 

BIEPST.21  Z,ZK  5  2P+2C  English 
 Garant předmětu:
 Pavel Hrabák
 Lecturer:
 Pavel Hrabák, Petr Novák
 Tutor:
 Pavel Hrabák, Petr Novák
 Supervisor:
 Department of Applied Mathematics
 Synopsis:

Students will learn the basics of probabilistic thinking, the ability to synthesize prior and posterior information and learn to work with random variables. They will be able to apply basic models of random variable distributions and solve applied probabilistic problems in informatics and computer science. Using the statistical induction they will be able to perform estimations of unknown distributional parameters from random sample characteristics. They will also be introduced to the methods for testing statistical hypotheses and determining the statistical dependence of two or more random variables.
 Requirements:

Basics of combinatorics and mathematical analysis.
 Syllabus of lectures:

1. Probability  random events, event space structure, probability of a random event and its basic properties.
2. Conditional probability  dependent and independent events, Bayes theorem.
3. Random variables  distribution function of a random variable, continuous and discrete distributions, quantiles, median.
4. Characteristics of random variables  expected value, variance, general moments, kurtosis and skewness.
5. Overview of basic distributions  binomial, geometric, Poisson, uniform, normal, exponential. Their basic properties.
6. Random vectors  joint and marginal statistics, correlation coefficient, dependence and independence of random variables.
7. Random vectors  conditional distributions, sums of random variables.
8. Limit theorems  laws of large numbers, central limit theorem.
9. Statistical estimation  classification and processing of data sets, graphical representation of data, random sample, point estimation, basic sample statistics, sample mean and variance.
10. Interval estimation  confidence intervals for expectation and variance.
11. Hypothesis testing  testing strategy, tests for expectation and variance, their modifications.
12. Application of statistical testing in computer science.
13. Correlation and regression analysis: Linear and quadratic regression, sample correlation.
 Syllabus of tutorials:

1. Basics of probability.
2. Conditional probability.
3. Random variables.
4. Basic characteristics of random variables.
5. Using basic distributions.
6. Random vectors  independence, covariance.
7. Random vectors  conditional distributions and sums.
8. Limit theorems
9. Processing of sets of data.
10. Statistical point estimation.
11. Interval estimation.
12. Hypotheses testing.
13. Regression and correlation analysis.
 Study Objective:

The goal of the module is to introduce the students to basics of probability theory and mathematical statistics while focusing on applications in informatics.
 Study materials:

1. Ahn H. : Probability and Statistics for Science and Engineering with Examples in R. Cognella, 2017. ISBN 9781516513987.
2. Johnson J. L. : Probability and Statistics for Computer Science. WileyInterscience, 2008. ISBN 470383429.
3. Bonselet Ch. : Probability, Statistics, and Random Signals. Oxford University Press, 2016. ISBN 9780190200510.
4. Grimmett G. R., Stirzaker D. R. : Probability and Random Processes (3rd Edition). Oxford University Press, 2001. ISBN 0198572239.
 Note:
 Timetable for winter semester 2023/2024:
 Timetable is not available yet
 Timetable for summer semester 2023/2024:
 Timetable is not available yet
 The course is a part of the following study plans:

 Bachelor specialization, Computer Engineering, 2021 (compulsory course in the program)
 Bachelor specialization, Information Security, 2021 (compulsory course in the program)
 Bachelor specialization, Software Engineering, 2021 (compulsory course in the program)
 Bachelor specialization, Computer Science, 2021 (compulsory course in the program)
 Bachelor specialization, Computer Networks and Internet, 2021 (compulsory course in the program)
 Bachelor specialization Computer Systems and Virtualization, 2021 (compulsory course in the program)