Syllabus
Introduction to probability theory and statistical induction.
Axiomatic definition of probability, computation of probability, conditional probability and Bayes formula.
Random variables and vectors and their distribution, characteristics of random variables.
Convergence in probability and in distribution, law of large numbers and central limit theorem, Markov, Čebyšev and Chernoff inequalities.
Applications of limit theorems and inequalities.
Statistical estimation based on limit theorems.
Annotation
Basic notions of the probability and statistics will be introduced and examples of applications will be given. It concerns especially of the notion of probability, random variable and of its distribution, independence, random sample and its descriptive characteristics, construction of estimators, testing of hypotheses and random number generation.
Emphasis will be especially on the practical use of above mentioned methods using freely available statistical software.