Subject description - BD5B01STP
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Explanatory Notes
Instructions
Web page:
https://math.fel.cvut.cz/en/people/heliskat/01pstD.html
Anotation:
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 targets:
Introduction to the theory of probability and mathematical statistics, and show them the computing methods together with their applications of praxis.
Content:
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. |
| 14. | | Hypotheses testing. |
Exercises outline:
| 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. |
| 14. | | Hypotheses testing. |
Literature:
| [1] | | M. Navara: Pravděpodobnost a matematická statistika. ČVUT, Praha 2007. |
| [2] | | V. Dupač, M. Hušková: Pravděpodobnost a matematická statistika. Karolinum, Praha 1999. |
Requirements:
Basic calculus, namely integrals.
Keywords:
Probability, statistics.
Subject is included into these academic programs:
| Page updated 16.4.2024 17:53:17, semester: Z,L/2023-4, Z/2024-5, Send comments about the content to the Administrators of the Academic Programs |
Proposal and Realization: I. Halaška (K336), J. Novák (K336) |