Classical finite models and the need of the rigid theory. Paradoxes and Natural Sciences

Combinatorics, cases of distinguishable and indistinguishable objects. Generation functions and other computational tools

Conditional probabilities, the independence of events and its formal properties. Bayesian approach for finite and infinite discrete cases

Heuristic non-finite models derived by means of the symmetry arguments. Algebra of events and the corresponding mathematical theory. Probabilities in discrete sample spaces and axiomatic approach

Different approaches to Probabilities: the model of von Mises and the classical model. General discrete model and quantum probability model

Moments and other characteristics of the random variables. Chebyshev inequalities. Whether the moments are always defined

he Law of Large Numbers and what Statistics can do. Sample space and several approaches in Statistics

Integral valued random variables and generating functions. Computational techniques

Basic discrete models and discrete random variables. Sequences of random variables. Random Walks model

Binomial distribution and its approximations in limit case. The idea of the Central Limit Theorem and its meaning for the Natural Sciences. An experimental illustrations

Distribution functions and the classification of random variables. Back to Statistics: the main problem of Classical statistics. Non-parametric criteria

Random variable from formal and heuristic points of view. Examples. Scalar and vector random variables and their properties. Mutual and group independence

Lebeg integration and computational formulas in general cases. Rademacher functions and the sequence of independent random variables. Kolmogorov’s axioms and other approaches

Sequences of random variables and several types of their limiting behaviour. Characteristic functions and their properties

Central Limit Theorem and its constraints. Gaussian and non-gaussian statistics. Mixtures and randomisations. Real data and the theory