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, PrenticeHall, 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
 Timetable for winter semester 2022/2023:

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 Thu Fri  Timetable for summer semester 2022/2023:
 Timetable 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)