Probability and Statistics

Course guarantor:

Jana Nosková

Lecturer:

Jana Nosková

Tutor:

Jana Nosková

Supervisor:

Department of Mathematics

Synopsis:

Fundamental concepts and terminology, random variables, descriptive and inferential statistics. Discrete and continuous random variables, normal distribution, log- normal distribution. Classical and nonparametric methods of estimation and hypotheses testing. Simple and multivariate linear regression.

Requirements:

The knowledge of simple and multivariate integration is required.

Syllabus of lectures:

1. Probability and conditional probability.

2. The Law of Total Probability and Bayes' Theorem.

3 Discrete random variable. Expectation, standard deviation, quantiles.

4. Binomial, Poisson and hypergeometrical distribution.

5. Continuous randam variables. Distribution function.

6. Uniform and exponential distribution.

7. Normal distribution. Log-normal distributioní.

8. Bivariate distribution. Correlation coefficient.

9. Distribution of a linear combination of multivarite normal distribution.

10. Hypothesis testing.

11. Nonparametric tests.

12. Simple linear regression.

13. Multivariate regression.

Syllabus of tutorials:

Exercises follow lectures.

Study Objective:

To be acquainted with basic ideas of mathematical statistics.

Study materials:

!Jarušková Daniela: Pravděpodobnost a matematická statistika , skripta ČVUT 2015, ISBN 80-01-02253-6

!Anděl Jiří: Základy matematické statistiky, MATFYZPRESS 2011,ISBN 978-80-7378-162-0

?Wasserman Larry: All of Statistics, Springer 2004,ISBN 978-0-387-40272-7

Note:

Time-table for winter semester 2024/2025:

	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
Wed	roomTH:C-221 10:00–11:50 (lecture parallel1) Thákurova 7 (budova FSv) roomTH:B-975 16:00–17:50 (lecture parallel1 parallel nr.102) Thákurova 7 (budova FSv)
Thu	roomTH:B-975 15:00–16:50 (lecture parallel1 parallel nr.101) Thákurova 7 (budova FSv)
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Geodézie a kartografie (compulsory course)
• Geodézie a kartografie (compulsory course)