Course Details

# Mathematics 4

BAA004 course is part of 9 study plans

BPC-SI Winter Semester 1st year

BPC-SI Winter Semester 1st year

BPC-SI Winter Semester 1st year

BPC-SI Winter Semester 1st year

BPC-SI Winter Semester 1st year

BPC-MI Winter Semester 1st year

BPC-EVB Winter Semester 1st year

BPA-SI Winter Semester 1st year

BKC-SI Winter Semester 1st year

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

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.

Knowledge

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.

Syllabus

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. Independent random variables.
4. 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, hypergeometric - 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.  Asymptotic test on the alternative distribution parameter.
12. Goodness-of-fit tests. Chi - square test. Basics of regression analysis.
13. Linear model.

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.

Language of instruction

Czech, English

Credits

5 credits

Semester

winter

Forms and criteria of assessment

course-unit credit and examination

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

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Offered to foreign students

To offer to students of all faculties

Course on BUT site

https://www.vut.cz/en/students/courses/detail/252904

Lecture

13 weeks, 2 hours/week, elective

Syllabus

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. Independent random variables.
4. 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, hypergeometric - 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. Asymptotic test on the alternative distribution parameter.
12. Goodness-of-fit tests. Chi - square test. Basics of regression analysis.
13. Linear model.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

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, hypergeometric.
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. Asymptotic test on the alternative distribution parameter.
13. Goodness-of-fit test.