Subject description - A2M01PMS

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A2M01PMS Probability and Statistics
Roles:P, V Extent of teaching:4+2
Department:13101 Language of teaching:CS
Guarantors:  Completion:Z,ZK
Lecturers:  Credits:8
Tutors:  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.

Webpage:

https://moodle.fel.cvut.cz/courses/A2M01PMS

Subject is included into these academic programs:

Program Branch Role Recommended semester
MPIB Common courses V –
MPEEM1 Technological Systems V 1
MPEEM5 Economy and Management of Electrical Engineering V 1
MPEEM4 Economy and Management of Power Engineering V 1
MPEEM3 Electrical Power Engineering V 1
MPEEM2 Electrical Machines, Apparatus and Drives V 1
MPKME1 Wireless Communication P 1
MPKME5 Systems of Communication P 1
MPKME4 Networks of Electronic Communication P 1
MPKME3 Electronics P 1
MPKME2 Multimedia Technology 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 10.8.2020 11:51:52, semester: Z,L/2020-1, L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)
Responsible person: doc. Ing. Jiří Jakovenko, Ph.D.