Statistics and Probability
Code  Completion  Credits  Range 

B6B01PRA  Z,ZK  5  2P+2S+1D 
 The course cannot be taken simultaneously with:
 Statistics and Probability (B6B01PST)
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

The students will be introduced to the theory of probability and mathematical statistics, namely to the basic computing methods and their applications in practice. The course covers the basic parts of probability and mathematical statistics. The first part is focused on classical probability, including conditional probability. The next part deals with the theory of random variables and their distributions, examples of the most important types of discrete and continuous distributions, numerical characteristics of random variables, their independence, sums and transformations. Probabilistic knowledge is then used in the description of statistical methods for estimating distribution parameters and testing hypotheses.
 Requirements:

Calculation of basic derivatives and integrals. Basics of combinatorics.
 Syllabus of lectures:

1. Random events, probability, probability space.
2. Conditional probability, Bayes' theorem, independent events.
3. Random variable  definition, distribution function, probability function, density.
4. Characteristics of random variables  expected value, variance and other moments.
5. Discrete random variable  examples and usage.
6. Continuous random variable  examples and usage.
7. Independence of random variables, covariance, correlation.
8. Transformation of random variables, sum of independent random variables (convolution).
9. Random vector, covariance and correlation.
10. Central limit theorem.
11. Random sampling and basic statistics.
12. Point estimates, maximum likelihood method and method of moments.
13. Confidence intervals.
14. Hypotheses testing.
 Syllabus of tutorials:

1. Combinatorics, random events, probability, probability space.
2. Conditional probability, Bayes' theorem, independent events.
3. Random variable  construction and usage of distribution function, probability function and density.
4. Characteristics of random variables  expected value, variance.
5. Discrete random variable  examples and usage.
6. Continuous random variable  examples and usage.
7. Independence of random variables, covariance, correlation.
8. Transformation of random variables, sum of independent random variables (convolution).
9. Random vector, joint and marginal distribution.
10. Central limit theorem.
11. Random sampling and basic statistics, point estimates, maximum likelihood method and method of moments.
12. Confidence intervals.
13. Hypotheses testing.
14. Reserve.
 Study Objective:

The students will be introduced to the theory of probability and mathematical statistics, namely to the basic computing methods and their applications in practice.
 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:
 https://math.fel.cvut.cz/en/people/heliskat/01pst.html
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Software Engineering and Technology (compulsory course in the program)
 Software Engineering and Technology (compulsory course in the program)
 Software Engineering and Technology (compulsory course in the program)
 Software Engineering and Technology (compulsory course in the program)
 Software Engineering and Technology (compulsory course in the program)