Probability and Statistics
Code  Completion  Credits  Range 

B6B01PST  Z,ZK  4  2P+2S+1D 
 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:

Calculation of basic derivatives and integrals.
 Syllabus of lectures:

1. Random events, probability, probability space.
2. Conditional probability, Bayes' theorem, independent events.
3. Random variable  definition, distribution function, density.
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.
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, density.
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.
13. Confidence intervals.
14. Hypotheses testing.
 Study Objective:

Introduction 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/01pstA7B01PST.html
 Timetable for winter semester 2019/2020:
 Timetable is not available yet
 Timetable for summer 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
Mon Tue Fri Thu Fri  The course is a part of the following study plans:

 Software Engineering and Technology (compulsory course in the program)