Probability and Statistics

Course guarantor:

Pavel Hrabák

Lecturer:

Daniel Vašata

Tutor:

Daniel Vašata

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 event, event space structure, probability of a random event and its basic properties. Conditional probability: Dependent and independent events, Bayes theorem.

2. Random variable: Distribution function of a random variable, continuous and discrete distributions, quantiles, median. Characteristics of position and shape: Mean value, variance, general moments, kurtosis and skewness.

3. Overview of basic distributions: binomial, Poisson, uniform, normal, exponential. Their basic properties. Probability applications. Hash functions, probabilistic algorithms.

4. Random vector: Joint and marginal statistics, correlation coefficient, dependence and independence of random variables. Descriptive statistics: Classification and processing of data sets, characteristics of position, variance, and shape, sampling moments, graphical representation of data.

5. Random sampling: Simple and stratified sampling, their distributions, basic sampling statistics, sample mean and variance, distributions (t-distribution, F-distribution, chi square). Parameter estimation: Confidence interval, point estimation, methods.

6. Hypothesis testing: Testing strategy, mean value and variance tests, some of their modifications. Application of statistical testing in CS. Non-parametric tests: Comparing distributions, Wilcoxon test, Smirnov-Kolmogorov test, goodness-of-fit test.

7. Analysis of variance: One-way and two-way classification, normality testing. Correlation and regression analysis: Linear and quadratic regression, sample correlation.

Syllabus of tutorials:

1. Elements of probability. Conditional probability. Random variable. Basic characteristics of random variables. Using basic distributions. Calculations of random variable characteristics. Hash functions.

2. Multidimensional random variables. Processing of sets of data. Random sampling. Parameter estimation. Hypotheses testing. Non-parametric tests. 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 978-1516513987.

2. Zvára, K., Štěpán, J. Pravděpodobnost a matematická statistika (5.vydání). Matfyzpress, 2013. ISBN 978-8073782184.

3. Johnson, J. L. Probability and Statistics for Computer Science. Wiley-Interscience, 2008. ISBN 470383429.

4. Bonselet, Ch. Probability, Statistics, and Random Signals. Oxford University Press, 2016. ISBN 978-0190200510.

5. Grimmett, G. R., Stirzaker, D. R., Probability and Random Processes (3rd Edition). Oxford University Press, 2001. ISBN 0-19-857223-9.

Note:

Further information:

https://courses.fit.cvut.cz/BI-PST/parttime/index.html

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Bachelor Specialization Information Security, part-time, in Czech, 2021 (compulsory course in the program)
• Bachelor Specialization Software Engineering, part-time, in Czech, 2021 (compulsory course in the program)
• Bachelor Specialization Computer Networks and Internet, part-time, in Czech, 2021 (compulsory course in the program)
• Bachelor Specialization Computer Systems and Virtualization, part-time, in Czech, 2021 (compulsory course in the program)
• Bachelor program, unspecified specialization, part-time, in Czech, 2021 (compulsory course in the program)