Description:

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.

Contents:

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.

Seminar contents:

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.

Recommended literature:

1. Ahn H. : Probability and Statistics for Science and Engineering with Examples in R. Cognella, 2017. ISBN 978-1516513987.
2. Johnson J. L. : Probability and Statistics for Computer Science. Wiley-Interscience, 2008. ISBN 470383429.
3. Bonselet Ch. : Probability, Statistics, and Random Signals. Oxford University Press, 2016. ISBN 978-0190200510.
4. Grimmett G. R., Stirzaker D. R. : Probability and Random Processes (3rd Edition). Oxford University Press, 2001. ISBN 0-19-857223-9.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar