CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Statistics and Probability

Code Completion Credits Range
BD5B01STP Z,ZK 6 14KP+6KC
Lecturer:
Kateřina Helisová (guarantor)
Tutor:
Kateřina Helisová (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

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.

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.

14. Hypotheses testing.

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.

14. Hypotheses testing.

Study Objective:

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

Study materials:

[1] M. Navara: Pravděpodobnost a matematická statistika. ČVUT, Praha 2007.

[2] V. Dupač, M. Hušková: Pravděpodobnost a matematická statistika. Karolinum, Praha 1999.

Note:
Further information: