Probability and Statistics

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Applied Mathematics

Synopsis:

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.

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, 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.

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. 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.

Note:

Further information:

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

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, 2015-2020 (compulsory course in the program)
• Bachelor branch Security and Information Technology, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Computer Science, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Computer Engineering, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Information Systems and Management, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Web and Software Engineering, spec. Software Engineering, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Web and Software Engineering, spec. Web Engineering, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Web and Software Engineering, spec. Computer Graphics, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Knowledge Engineering, in Czech, 2018-2020 (compulsory course in the program)