Statistics and Probability
Code  Completion  Credits  Range 

BD5B01STP  Z,ZK  6  14KP+6KC 
 Course guarantor:
 Lecturer:
 Tutor:
 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:
 https://math.fel.cvut.cz/en/people/heliskat/01pstD.html
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Electrical Enginnering, Electronics and Communications (compulsory course in the program)