Introduction to probability theory and mathematical statistics. Determinism and chance. Axiomatic definition. Random variable and its distribution function. Discrete and continuous distributions. Quintiles. Random vectors. Conditioning and independence. Functions of random variables. Characteristics of random variables, weak law of large numbers. The role of mathematical statistics, the population and sample. Random selection. Point and interval estimates. Hypothesis testing. Goodness. Non-parametric tests.
Contents:
1. Motivational lecture. Determinism and randomness.
2. Random variable and distribution function.
3. Discrete distributions.
4. Continuous distributions.
5. Random vectors, conditioning and independence.
6. Random vectors, characteristics, functions of random variables.
7. The role of mathematical statistics.
8. Parameter estimation.
9. Testing hypotheses in a normal distribution.
10. Non-parametric tests.
11. Analysis of variance.
12. Principles of experimental design.
Recommended literature:
1. Chatfield C.: Statistics for Technology, 3rd edition, Chapman and Hall, London, 1992.
2. Rogalewicz V.: Pravděpodobnost a statistika pro inženýry. Skriptum ČVUT, 2. vydání, 2007. (in Czech)
3. http://wiki.stat.ucla.edu/socr/index.php/EBook