Probability and Statistics

Garant předmětu:

Přednášející:

Cvičící:

Předmět zajišťuje:

katedra aplikované matematiky

Anotace:

The 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 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 of determining the statistical dependence of two or more random variables.

Požadavky:

Basics of combinatorics and mathematical analysis.

Osnova přednášek:

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, characteristics of position, variance and shape, sampling moments, graphical representation of data.

10. Point estimation: Random sample, basic sample statistics, sample mean and variance, distributions (t-distribution, F-distribution, chi square).

11. Interval estimation: Confidence intervals for expectation and variance.

12. Hypothesis testing: Testing strategy, tests for expectation and variance, their modifications. Application of statistical testing in CS.

13. Correlation and regression analysis: Linear and quadratic regression, sample correlation.

Osnova cvičení:

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.

Cíle studia:

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

Studijní materiály:

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.

Poznámka:

Information about the course and courseware are available athttps://courses.fit.cvut.cz/BIE-PST/

Další informace:

https://courses.fit.cvut.cz/BIE-PST/

Pro tento předmět se rozvrh nepřipravuje

Předmět je součástí následujících studijních plánů:

• Bachelor branch Security and Information Technology, in English, 2015-2020 (povinný předmět programu)
• Bachelor branch Web and Software Engineering, spec. Software Engineering, in English, 2015-2020 (povinný předmět programu)
• Bachelor branch Computer Science, in English, 2015-2020 (povinný předmět programu)
• Bachelor branch Computer Science, in English, 2015-2020 original version (povinný předmět programu)