Probability and Statistics

Lecturer:

Jitka Hanousková

Tutor:

Jitka Hanousková

Supervisor:

Department of Applied Mathematics

Synopsis:

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.

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.

2. Conditional probability: Dependent and independent events, Bayes theorem.

3. Random variable: Distribution function of a random variable, continuous and discrete distributions, quantiles, median.

4. Characteristics of position and shape: Mean value, variance, general moments, kurtosis and skewness.

5. Overview of basic distributions: binomial, Poisson, uniform, normal, exponential. Their basic properties.

6. Probability applications. Hash functions, probabilistic algorithms.

7. Random vector: Joint and marginal statistics, correlation coefficient, dependence and independence of random variables.

8. Descriptive statistics: Classification and processing of data sets, characteristics of position, variance, and shape, sampling moments, graphical representation of data.

9. Random sampling: Simple and stratified sampling, their distributions, basic sampling statistics, sample mean and variance, distributions (t-distribution, F-distribution, chi square).

10. Parameter estimation: Confidence interval, point estimation, methods.

11. Hypothesis testing: Testing strategy, mean value and variance tests, some of their modifications. Application of statistical testing in CS.

12. Non-parametric tests: Comparing distributions, Wilcoxon test, Smirnov-Kolmogorov test, goodness-of-fit test.

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

Syllabus of tutorials:

1. Correlation analysis.

2. Elements of probability.

3. Conditional probability.

4. Random variable.

5. Basic characteristics of random variables.

6. Using basic distributions.

7. Calculations of random variable characteristics.

8. Hash functions.

9. Multidimensional random variables.

10. Processing of sets of data.

11. Random sampling.

12. Parameter estimation.

13. Hypotheses testing.

14. Non-parametric tests.

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.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Fri	roomTH:A-1029 Hanousková J. 09:15–10:45 (lecture parallel1) Dejvice
Thu
Fri

The course is a part of the following study plans:

• Information Systems and Management (Presented in English) (compulsory course in the program)
• Information Technologies (Presented in English) (compulsory course in the program)
• Computer Engineering (Presented in English) (compulsory course in the program)
• Software Engineering (Presented in English) (compulsory course in the program)
• Computer Science (Presented in English) (compulsory course in the program)
• Web and Multimedia (Presented in English) (compulsory course in the program)
• Informatics (Presented in English) (compulsory course in the program)