Course Details

Probability and statistics

Academic Year 2025/26

BAA011 course is part of 1 study plan

​ BPC-GK Summer Semester 2nd year

Course Guarantor

Ing. Pavel Špaček, Dr.

Institute

Institute of Mathematics and Descriptive Geometry

Language of instruction

Czech

Credits

4 credits

Semester

summer

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/289945

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 of random variable. Marginal random vector and its distribution.
  • 4. Independent random variables. Numeric characteristics of random variable: mean and variance, quantiles. Rules of calculation mean and variance.
  • 5. Numeric characteristics of random vectors: covariance, correlation coefficient. Normal distribution - definition, using.
  • 6. Chi-square distribution, Student´s distribution. Random sampling, sample statistics.
  • 7. Point estimation of distribution parameters, desirable properties of an estimator - definition, interpretation.
  • 8. Confidence interval for distribution parameters.
  • 9. Fundamentals of hypothesis testing. Tests of hypotheses for normal distribution parameters.
  • 10. Goodness-of-fit tests.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

  • 1. Empirical distributions. Histogram. Probability and density distributions.
  • 2. Probability. Cumulative distribution.
  • 3. Relationships between probability, density and cumulative distributions.
  • 4. Transformation of random variable.
  • 5. Calculation of mean, variance and quantiles of random variable. Calculation rules of mean and variance.
  • 6. Correlation coefficient. Calculation of probability in some cases of discrete probability distributions - alternative, binomial, Poisson.
  • 7. Calculation of probability for normal distribution. Work with statistical tables. Calculation of point estimators.
  • 8. Confidence interval for normal distribution parameters.
  • 9. Tests of hypotheses for normal distribution parameters.
  • 10. Goodness-of-fit tests.