|
Lecturer(s)
|
-
Marek Jaroslav, Mgr. Ph.D.
-
Hrůzová Klára, Mgr. Ph.D.
-
Rak Josef, RNDr. Ph.D.
-
Javůrek Milan, doc. Ing. CSc.
|
|
Course content
|
Statistics - summary Probability theory. Random events and elementary event space. Probability. Axiomatic, classical, geometrical and statistical definition of probability. Bertrand´s paradox. Conditional probability, independent random events. The complete probability. One-dimensional and multi-dimensional random variable. Continues and discrete random variable. Probability function, probability density function, distribution function. Marginal and conditional distribution. Moments, measures of position and measures of dispersion of one-dimensional and two-dimensional random distribution. Selected distributions of discrete and continuous one-dimensional random variables : two point, binomial, Poisson distribution, uniform, exponential, normal distribution, Chi-square, t, F distribution. Chebyshev theorem, central limit theorem. Statistical methods Population and random sample. Empirical distribution. Sample moments, sample arithmetic mean, sample variation. Estimation methods.Point estimation. Interval estimation. Confidence intervals for expected value and for variance . Lower and upper control limits. Statistical hypothesis testing.A null hypothesis, an alternative hypothesis, the level of significance of the test, the critical region, one-sided tests, two-sided tests. Testing the hypothesis concerning the expected value of the normal distribution, testing the hypothesis concerning the variance of the normal random variable. The u-test, t-test, F-test. Non-parametric hypothesis testing. The sign test, Wilcoxon test. The chi-square test for goodness of fit. The least square method. Linear regression model by the least square method. Testing significance of regression coefficient and intercept. Confidence intervals of regression coefficient and intercept. Correlation. Measures of dependence. Study of significance of correlations.
|
|
Learning activities and teaching methods
|
|
Monologic (reading, lecture, briefing)
|
|
Learning outcomes
|
The aim of the course is to acquaint the students with theory of probability and statistical principles in order to apply it in real situations.
Student will be able to use statistical methods and theory of probability in real situations.
|
|
Prerequisites
|
Good mathematical skills. Good integral and differential calculus knowledge.
|
|
Assessment methods and criteria
|
Oral examination, Written examination
Requirement: 80% participation + credit test. For a repeating students: Recurring student can choose either a 80% participation and recognition test from last year, or at least 50% attendance and a new credit test.
|
|
Recommended literature
|
-
Fahrmeir und koll. Statistik. Springer - Verlag. Berlin, 2004.
-
Kubanová, J., Linda, B. Sbírka příkladů z pravděpodobnosti. Statis, 2004.
-
Kubanová, J. Statistické metody pro ekonomickou a technickou praxi. Statis, 2004.
-
Sirvastava, M., S. Methods of multoivariate statistics. Wiley, New York, 2002.
|