Probability and Statistics

Přednášející:

Jaroslav Tišer (gar.)

Cvičící:

Jaroslav Tišer (gar.)

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:

A.F.Karr: Probability, Springer Texts in Statistics, Springer Verlag 1993

K.L.Chung: A course in probability theory, Academic Press 1974

Poznámka:

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

Další informace:

Pro tento předmět se rozvrh nepřipravuje

Předmět je součástí následujících studijních plánů:

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