Probability and Statistics

Course guarantor:

Kateřina Helisová

Lecturer:

Kateřina Helisová, Bogdan Radović

Tutor:

Kateřina Helisová, Bogdan Radović

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 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	roomT2:C4-78 Radović B. 09:15–10:45 (lecture parallel1) Dejvice T2:C4-78roomT2:C4-78 Radović B. 12:45–14:15 (lecture parallel1 parallel nr.1) Dejvice T2:C4-78 roomT2:C4-78 Radović B. 11:00–12:30 (lecture parallel1) Dejvice T2:C4-78
Tue
Wed
Thu
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Electrical Engineering and Computer Science (EECS) (compulsory course in the program)
• Electrical Engineering and Computer Science (EECS) (compulsory course in the program)