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ČESKÉ VYSOKÉ UČENÍ TECHNICKÉ V PRAZE
STUDIJNÍ PLÁNY
2019/2020

Probability and Statistics

Předmět není vypsán Nerozvrhuje se
Kód Zakončení Kredity Rozsah Jazyk výuky
AE1M01MPS Z,ZK 8 4+2
Přednášející:
Cvičící:
Předmět zajišťuje:
katedra matematiky
Anotace:

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.

Požadavky:

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

Osnova přednášek:

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.

Osnova cvičení:

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.

Cíle studia:

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

Studijní materiály:

[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.

Poznámka:

Rozsah výuky v kombinované formě studia: 28p+6s

Další informace:
http://math.feld.cvut.cz/helisova/01pstimfe.html
Pro tento předmět se rozvrh nepřipravuje
Předmět je součástí následujících studijních plánů:
Platnost dat k 18. 10. 2019
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