Počet kreditů 4
Vyučováno v Summer
Rozsah výuky 2P+2S+1D
Garant předmětu
Přednášející
Cvičící

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.

Calculation of basic derivatives and integrals.

Introduction the students to the theory of probability and mathematical statistics, and show them the computing methods together with their applications of praxis.

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.

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.

[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.

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