Probability and Statistics

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

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.

Requirements:

The requirement for receiving the credit is an active participation in the tutorials.

Syllabus of lectures:

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.

Syllabus of tutorials:

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.

Study Objective:

The aim of the course is to introduce students to basics of probability and statistics.

Study materials:

[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.

Note:

Further information:

http://math.feld.cvut.cz/helisova/01pstAD2M01PMS.html

No time-table has been prepared for this course

The course is a part of the following study plans:

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• Elektrotechnika, energetika a management - Ekonomika a řízení energetiky_145106 (elective course)
• Elektrotechnika, energetika a management - Ekonomika a řízení elektrotechniky_145126 (elective course)
• Komunikace, multimédia a elektronika - Bezdrátové komunikace_145152 (compulsory course in the program)
• Komunikace, multimédia a elektronika - Multimediální technika_145209 (compulsory course in the program)
• Komunikace, multimédia a elektronika - Elektronika_145231 (compulsory course in the program)
• Komunikace, multimédia a elektronika - Sítě elektronických komunikací_145248 (compulsory course in the program)
• Kybernetika a robotika - Robotika_145304 (elective course)
• Kybernetika a robotika - Senzory a přístrojová technika_145332 (elective course)
• Kybernetika a robotika - Systémy a řízení_145356 (elective course)
• Otevřená informatika - Umělá inteligence_145417 (elective course)
• Otevřená informatika - Počítačové inženýrství_145440 (elective course)
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• Otevřená informatika - Softwarové inženýrství_145534 (elective course)
• Kybernetika a robotika - Letecké a kosmické systémy (elective course)
• Komunikace, multimédia a elektronika - Komunikační systémy (compulsory course in the program)