Course Details

Mathematics 4

Academic Year 2024/25

BAA004 course is part of 9 study plans

​ BPC-SI / S Winter Semester 3rd year

​ BPC-SI / K Winter Semester 3rd year

​ BPC-SI / E Winter Semester 3rd year

​ BPC-SI / M Winter Semester 3rd year

​ BPC-SI / V Winter Semester 3rd year

​ BPC-MI Winter Semester 2nd year

​ BPC-EVB Winter Semester 3rd year

​ BKC-SI Winter Semester 3rd year

​ BPA-SI Winter Semester 3rd year

Course Guarantor

Ing. Jan Holešovský, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Language of instruction

Czech, English

Credits

5 credits

Semester

winter

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

To offer to students of all faculties

Course on BUT site

https://www.vut.cz/en/students/courses/detail/281403

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.