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Course detail

Mathematics 4

Course unit code: FAST-BA004
Academic year: 2017/2018
Type of course unit: compulsory
Level of course unit: Bachelor's (1st cycle)
Year of study: 3
Semester: winter
Number of ECTS credits:
Learning outcomes of the course unit:
Student will be able to solve simple practical probability problems and to use basic statistical methods from the fields of interval estimates, testing parametric and non-parametric statistical hypotheses, and linear models.
Mode of delivery:
90 % face-to-face, 10 % distance learning
Prerequisites:
Basics of the theory of one- and more-functions (derivative, partial derivative, limit and continuous functions, graphs of functions). Calculation of definite integrals, double and triple integrals, knowledge of their basic applications.
Co-requisites:
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
Discrete and continuous random variable and vector, probability function, density function, probability, cumulative distribution, transformation of random variables, independence of random variables, numeric characteristics of random variables and vectors, special distribution laws. Random sample, point estimation of an unknown distribution parameter and its properties, interval estimation of a distribution parameter, testing of statistical hypotheses, tests of distribution parameters, goodness-of-fit tests, basics of regression analysis.
Recommended or required reading:
Not applicable.
Planned learning activities and teaching methods:
Not applicable.
Assesment methods and criteria linked to learning outcomes:
Not applicable.
Language of instruction:
Czech, English
Work placements:
Not applicable.
Course curriculum:
1. Continuous and discrete random variable (vector), probability function, density function. Probability.
2. Properties of probability. Cumulative distribution and its properties.
3. Relationships between probability, density and cumulative distributions. Marginal random vector.
4. Independent random variables. Numeric characteristics of random variables: mean and variance, standard deviation, variation coefficient, modus, quantiles. Rules of calculation mean and variance.
5. Numeric characteristics of random vectors: covariance, correlation coefficient, covariance and correlation matrices.
6. Some discrete distributions - discrete uniform, alternative, binomial, Poisson - definition, using.
7. Some continuous distributions - continuous uniform, exponential, normal, multivariate normal - definition applications.
8. Chi-square distribution, Student´s distribution - definition, using. Random sampling, sample statistics.
9. Distribution of sample statistics. Point estimation of distribution parameters, desirable properties of an estimator.
10. Confidence interval for distribution parameters.
11. Fundamentals of hypothesis testing. Tests of hypotheses for normal distribution parameters.
12. Goodness-of-fit tests. Chi - square test. Basics of regression analysis.
13. Linear model.
Aims:
The students should get an overview of teh basic properties of probability to be able to deal with simple practical problems in probability. They should get familiar with the basic statistical methods used for interval estimates, testing statistical hypotheses, and linear model.
Specification of controlled education, way of implementation and compensation for absences:
Extent and forms are specified by guarantor’s regulation updated for every academic year.

Type of course unit:

Lecture: 26 hours, optionally
Teacher / Lecturer: RNDr. Helena Koutková, CSc.
seminars: 26 hours, compulsory
Teacher / Lecturer: RNDr. Helena Koutková, CSc.

The study programmes with the given course