Course Details

Mathematics 4

BAA004 course is part of 9 study plans

Bc. full-t. program BPC-EVB compulsory Winter Semester 3rd year 5 credits

Bc. full-t. program BPC-SI > spV compulsory Winter Semester 3rd year 5 credits

Bc. full-t. program BPC-SI > spM compulsory Winter Semester 3rd year 5 credits

Bc. full-t. program BPC-SI > spK compulsory Winter Semester 3rd year 5 credits

Bc. full-t. program BPC-SI > spS compulsory Winter Semester 3rd year 5 credits

Bc. full-t. program BPC-SI > spE compulsory Winter Semester 3rd year 5 credits

Bc. full-t. program BPC-MI compulsory Winter Semester 2nd year 5 credits

Bc. full-t. program BPA-SI compulsory Winter Semester 3rd year 5 credits

Bc. combi. program BKC-SI compulsory Winter Semester 3rd year 5 credits

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.

Course Guarantor

RNDr. Helena Koutková, CSc.

Institute

Institute of Mathematics and Descriptive Geometry

Learning outcomes

Student will be able to solve simple practical probability problems and use basic statistical methods for interval estimates, testing parametric and non-parametric statistical hypotheses and linear models.

Prerequisites

Basic knowledge of the theory of one and more functions (derivative, partial derivative, limit and continuous functions, graphs of functions). Ability to calculate definite integrals, double and triple integrals and knowledge of their basic applications.

Corequisites

Not required.

Planned educational activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations - lectures, seminars.

Forms and criteria of assessment

Students will receive credit based on attendance in practise classes and passing of a written test with at least 50% score. A written exam with a pass score of at least 50% will follow. The exam will last 90 minutes. It will consist of three practical (calculations) tasks and one task with theoretical questions.

Objective

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 instruction, the form of instruction, and the form of compensation of the absences

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

Lecture

2 hours/week, 13 weeks, elective

Syllabus of lectures

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.

Practice

2 hours/week, 13 weeks, compulsory

Syllabus of practice

1. Empirical probability and density distributions. Histogram.
2. Probability and density distributions. Probability.
3. Cumulative distribution. Relationships between probability, density and cumulative distributions.
4. Transformation of random variable.
5. Marginal and simultaneous random vector. Independence of random variables.
6. Calculation of mean, variance, standard deviation, variation coefficient, modus and quantiles of a random variable. Calculation rules of mean and variance.
7. Correlation coefficient. Test.
8. Calculation of probability in some cases of discrete probability distributions - alternative, binomial, Poisson.
9. Calculation of probability for normal distribution. Work with statistical tables.
10. Calculation of sample statistics. Application problems for their distribution.
11. Confidence interval for normal distribution parameters.
12. Tests of hypotheses for normal distribution parameters.
13. Goodness-of-fit test.