Random Events – Preliminary remarks – random events and operations performed on them – the system of axioms of the theory of probability – conditional probability – Bayes theorem – Independent Events – Random variables – the concept of a random variable – the distribution function – random variables of the discrete type and the continuous type – functions of random variables – Multidimensional random variables – marginal distributions – conditional distributions – Independent random variables – Parameters of the distributions of a random variable – expected values – moments – the Chebyshev inequality – absolute moments.

Characteristic functions – Properties of characteristic functions – the characteristic function and moments – semi-invariants – the characteristic function of the sum of independent random variables – Determination of the distribution function of multidimensional random vectors – probability – generating functions – some probability distributions - One point and two point distributions – the Bernoulli scheme. The binomial distribution. The generalized binomial distributions and the Poisson distributions.

Some probability distributions – the uniform distribution - the normal distribution – the gamma distribution – the Cauchy and Laplace distributions – Limit theorems – preliminary remarks – Stochastic convergence – Bernoulli‘s law of large numbers - the convergence of a sequence of distribution functions – the Levy-Cramer theorem – The de Moivre Laplace theorem – the Lindeberg-Levy theorem.

Sample moments and their functions – the notion of a sample – the notion of a Statistic – the distribution of the arithmetic mean of independent normally distributed random variables – the 2 distribution – the distribution of the statistic ( X, S) – student‘s t-distribution – Significance tests – the concept of a statistical test – parametric tests for small samples – parametric tests for large samples – the 2 test- independent tests by contingency tables.

The theory of Estimation – preliminary notions – Consistent estimates – unbiased estimates – the sufficiency of an estimate – the efficiency of an estimates – Asymptotically most efficient estimates – methods of finding estimates – confidence intervals – Theory of Hypothesis testing – preliminary remarks – the power function and the OC function.