Probability and Statistics
- Garant předmětu:
- Department of Applied Mathematics
Students are introduced to elements of probability thinking, ability of the synthesis both prior and posterior information and use to work with random variables. They will be able to apply correctly basic models of the distribution of random variables and to solve applied probability problems in the area of informatics and computer science. Using statistical inference methods, they master methods of statistical inference to estimate unknown population parameters on the basis of sample. They get acquainted with basic methods of the determination of possible statistical dependence of two or more random variables.
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 deliver students the standard basics of the probability theory and statistics while paying attention to typical applications in informatics.
- Study materials:
1. Johnson, J. L. ''Probability and Statistics for Computer Science''. Wiley-Interscience, 2008. ISBN 0470383429.
2. Li, X. R. ''Probability, Random Signals, and Statistics''. CRC, 1999. ISBN 0849304334.
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans:
- Bachelor program Informatics, unspecified branch, in Czech, part-time, 2015 – 2021 (compulsory course in the program)
- Bachelor branch Security and Information Technology, in Czech, part-time, 2015 - 2019 (compulsory course in the program)
- Bachelor branch Web and Software Engineering, spec. Software Engin., in Czech, part-time, 2015–2020 (compulsory course in the program)
- Bachelor branch Security and Information Technology, part-time, in Czech, 2020 (compulsory course in the program)
- Bachelor branch Security and Information Technology, in Czech, part-time, 2015 commuters (compulsory course in the program)