Probability and Statistics

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Technical Mathematics

Synopsis:

Explanation of the concept of probability space, conditional probability, Bayes theorem. Work with random variables and description of basic probability models. Explanation of methods of statistical induction and description of basic methods in statistical data analysis, testing of statistical hypotheses and regression analysis.

Requirements:

Syllabus of lectures:

Probability space and probability measure.

• Random variable. Probability distribution and its characteristics.

• Selected discrete and continuous probability models.

• Random vector, characteristics of random vector.

• Transformation of random variable.

• Law of large numbers, central limit theorem.

• Statistical induction primciple, sampling.

• Sample charakteristics. Frequency analysis.

• Point estimators, estimation of sample characteristics.

• Confidence interval.

• Testing of hypothesis.

• Goodness-of-fit tests.

• Nonparametric testing.

Syllabus of tutorials:

Probability space and probability measure.

• Random variable. Probability distribution and its characteristics.

• Selected discrete and continuous probability models.

• Random vector, characteristics of random vector.

• Transformation of random variable.

• Law of large numbers, central limit theorem.

• Statistical induction primciple, sampling.

• Sample charakteristics. Frequency analysis.

• Point estimators, estimation of sample characteristics.

• Confidence interval.

• Testing of hypothesis.

• Goodness-of-fit tests.

• Nonparametric testing.

Study Objective:

Study materials:

Grinstead, Ch. M., Snell, J. L.: (2011). Introduction to Probability. Available in Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/introduction-to-probability

Ash, R. B. (2008). Basic probability theory. Available at: https://faculty.math.illinois.edu/~r-ash/BPT/BPT.pdf

Lane D. M. et al. (2018). Introduction to Statistics. Available in Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/introduction-to-statistics

Isotalo J. (2017). Basics of Statistics. Available at: https://www.mv.helsinki.fi/home/jmisotal/BoS.pdf

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: