### Probability and Statistics

##### B232 - Summer 23/24
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#### Probability and Statistics - BE5B01PRS

 Credits 7 Semesters Winter Completion Assessment + Examination Language of teaching English Extent of teaching 4P+2S
Annotation
Introduction to the theory of probability, mathematical statistics and computing methods together with their applications of praxis.
Study targets
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.
Course outlines
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.
Exercises outlines
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.
Literature
[1] Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990.
[2] Stewart W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press 2009.
Requirements
Basic calculus, namely integrals.