CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Probability and Statistics

Code Completion Credits Range Language
BE5B01PRS Z,ZK 7 4P+2S English
Lecturer:
Kateřina Helisová (guarantor)
Tutor:
Kateřina Helisová (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

Introduction to the theory of probability, mathematical statistics and computing methods together with their applications of praxis.

Requirements:

Basic calculus, namely integrals.

Syllabus of lectures:

1. Random events, probability, probability space.

2. Conditional probability, Bayes' theorem, independent events.

3. Random variable - definition, distribution function.

4. Characteristics of random variables.

5. Discrete random variable - examples and usage.

6. Continuous random variable - examples and usage.

7. Independence of random variables, sum of independent random variables.

8. Transformation of random variables.

9. Random vector, covariance and correlation.

10. Central limit theorem.

11. Random sampling and basic statistics.

12. Point estimation, method of maximum likelihood and method of moments, confidence intervals.

13. Confidence intervals and hypotheses testing.

14. Markov chains.

Syllabus of tutorials:

1. Random events, probability, probability space.

2. Conditional probability, Bayes' theorem, independent events.

3. Random variable - definition, distribution function.

4. Characteristics of random variables.

5. Discrete random variable - examples and usage.

6. Continuous random variable - examples and usage.

7. Independence of random variables, sum of independent random variables.

8. Transformation of random variables.

9. Random vector, covariance and correlation.

10. Central limit theorem.

11. Random sampling and basic statistics.

12. Point estimation, method of maximum likelihood and method of moments, confidence intervals.

13. Confidence intervals and hypotheses testing.

14. Markov chains.

Study Objective:

The aim is to introduce the students to the theory of probability and mathematical statistics, and show them the computing methods together with their applications of praxis.

Study materials:

[1] Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990.

[2] Stewart W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press 2009.

Note:
Further information:
http://math.feld.cvut.cz/helisova/01pstimfe.html
Time-table for winter semester 2019/2020:
 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 roomT2:C4-78Helisová K.12:45–14:15(lecture parallel1)DejviceT2:C4-78roomT2:C4-78Helisová K.16:15–17:45(lecture parallel1parallel nr.1)DejviceT2:C4-78 roomT2:C4-78Helisová K.14:30–16:00(lecture parallel1)DejviceT2:C4-78
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-08-04
For updated information see http://bilakniha.cvut.cz/en/predmet4356306.html