Subject description - A1M01MPS
Summary of Study |
Summary of Branches |
All Subject Groups |
All Subjects |
List of Roles |
Explanatory Notes
Instructions
| A1M01MPS | Probability and Statistics | Extent of teaching: | 4+2 | ||
|---|---|---|---|---|---|
| Guarantors: | Roles: | P,V | Language of teaching: | CS | |
| Teachers: | Completion: | Z,ZK | |||
| Responsible Department: | 13101 | Credits: | 8 | Semester: | Z |
Anotation:
The course covers probability and basic statistics. First classical probability is introduced, then theory of random variables is developed including examples of the most important types of discrete and continuous distributions. Next chapters contain moment generating functions and moments of random variables, expectation and variance, conditional distributions and correlation and independence of random variables. Statistical methods for point estimates and confidence intervals are investigated.Study targets:
The aim of the course is to introduce students to basics of probability and statistics.Course outlines:
| 1. | Events and probability. | |
| 2. | Sample spaces. | |
| 3. | Independent events, conditional probability, Bayes' formula. | |
| 4. | Random variable, distribution functin, quantile function, moments. | |
| 5. | Independence of random variables, sum of independent random variables. | |
| 6. | Transformation of random variables. | |
| 7. | Random vector, covariance and correlation. | |
| 8. | Chebyshev's inequality and Law of large numbers. | |
| 9. | Central limit theorem. | |
| 10. | Random sampling and basic statistics. | |
| 11. | Point estimation, method of maximum likehood and method of moments, confidence intervals. | |
| 12. | Test of hypotheses. | |
| 13. | Testing of goodness of fit. |
Exercises outline:
| 1. | Events and probability. | |
| 2. | Sample spaces. | |
| 3. | Independent events, conditional probability, Bayes' formula. | |
| 4. | Random variable, distribution functin, quantile function, moments. | |
| 5. | Independence of random variables, sum of independent random variables. | |
| 6. | Transformation of random variables. | |
| 7. | Random vector, covariance and correlation. | |
| 8. | Chebyshev's inequality and Law of large numbers. | |
| 9. | Central limit theorem. | |
| 10. | Random sampling and basic statistics. | |
| 11. | Point estimation, method of maximum likehood and method of moments, confidence intervals. | |
| 12. | Test of hypotheses. | |
| 13. | Testing of goodness of fit. |
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:
The requirement for receiving the credit is an active participation in the tutorials. Subject is included into these academic programs:| Program | Branch | Role | Recommended semester |
| MPIB | Common courses | V | – |
| MPKME1 | Wireless Communication | V | 1 |
| MPKME5 | Systems of Communication | V | 1 |
| MPKME4 | Networks of Electronic Communication | V | 1 |
| MPKME3 | Electronics | V | 1 |
| MPKME2 | Multimedia Technology | V | 1 |
| MPEEM1 | Technological Systems | P | 1 |
| MPEEM3 | Electrical Power Engineering | P | 1 |
| MPEEM2 | Electrical Machines, Apparatus and Drives | P | 1 |
| MPKYR4 | Aerospace Systems | V | 1 |
| MPKYR1 | Robotics | V | 1 |
| MPKYR3 | Systems and Control | V | 1 |
| MPKYR2 | Sensors and Instrumentation | V | 1 |
| Page updated 16.12.2019 12:52:21, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |