714-0368/04 – Mathematics III (MIII)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
| Subject guarantor | Ing. Petra Schreiberová, Ph.D. | Subject version guarantor | Mgr. Petr Otipka, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | Czech |
| Year of introduction | 2010/2011 | Year of cancellation | 2019/2020 |
| Intended for the faculties | FS | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
The goal of the course is to serve as a theoretical and practical base to understand the importance of the basic notions in probability, and teach the student statistical way of thinking as a mean of understanding real life processes, introduce basic methods of collecting and analysing statistical data, and show the student how to use these general methods in other courses of study and in professional career.
The graduate of this course should be able:
• understand and use basic notions in combinatorics and probability theory
• formulate questions, which can be answered based on the given data, for this purpose learn the principles of collecting, processing data and presentation of relevant values and results
• choose and use suitable statistical methods for data analysis
• suggest and evaluate conclusions (inference) and predictions obtained from data
Teaching methods
Lectures
Seminars
Tutorials
Project work
Other activities
Summary
Probabilities of random events: axioms of probability, conditional probability,
independence. Random variables: discrete random variables, continuous random
variables, expected values. Important practical distributions of discrete and
continuous random variables.Estimating of parameters of population. Testing of
hypotheses. Exercises - EXCEL.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Požadavky pro udělení zápočtu a zkoušky
Zápočet:
Podmínky pro udělení zápočtu:
Za účast na konzultacích může student získat 5 - 20 b, v případě neúčasti může student získat 5 b za zpracování zadaného programu.
Kombinovaná zkouška:
Podmínkou pro účast na zkoušce je zapsaný zápočet z příslušného předmětu.
Písemná část zkoušky bude hodnocena 0 - 60 b, za její úspěšné absolvování bude považován zisk 25 b.
Ústní část zkoušky bude hodnocena 0 - 20 b, za její úspěšné absolvování bude považován zisk 5 b.
E-learning
Other requirements
Syllabus of lectures
=================
I. Probability
--------------------
Combinatorics.
Random events, operations with them, sample space.
Definitions of probability events - classical, geometrical, statistics.
Conditional probability, Bayes' theorem.
Bernoulli independent repeated trials.
II. Discrete random variable and continuous random variable.
----------------------------------------------------------------------------------------
Functions of random variables. Moment-generating function, quantiles.
Discrete probability distribution.
Continuous probability distribution.
Random vector. The probability distribution. Expected value, covariance, coefficient of correlation.
III. Statistics.
Statistical methods, descriptive statistics
Observed data. Point estimators, interval estimators.
Statistical hypothesis testing – the testing process, interpretation, importance.
Parametric and non-parametric tests.
Correlation and regression analysis.
Time series.
Forecasting. Time series methods.
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Syllabus of lectures
=================
I. Probability
--------------------
Combinatorics.
Random events, operations with them, sample space.
Definitions of probability events - classical, geometrical, statistics.
Conditional probability, Bayes' theorem.
Bernoulli independent repeated trials.
II. Discrete random variable and continuous random variable.
----------------------------------------------------------------------------------------
Functions of random variables. Moment-generating function, quantiles.
Discrete probability distribution.
Continuous probability distribution.
Random vector. The probability distribution. Expected value, covariance, coefficient of correlation.
III. Statistics.
Statistical methods, descriptive statistics
Observed data. Point estimators, interval estimators.
Statistical hypothesis testing – the testing process, interpretation, importance.
Parametric and non-parametric tests.
Correlation and regression analysis.
Time series.
Forecasting. Time series methods.
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction