Basics of probability

Comparing approaches of probability theory and statistics, the game of poker, event, sample space, mathematical module,, intersection and union of events, impossible and sure events, axiomatic definition of probability, properties of probability

Probability types

Classical probability, discrete probability, geometric probability, sigma field of events, probabilistic space, conditional probability, independent events, law of total probability, law of inverse probability

Random variable and distribution function

Definition and examples of a random variable, probability distribution function, properties of a distribution function, discrete random variables, probability function, continuous random variable, density function

Number characteristics of random variables

Expectancy, variance, standard deviation, quantiles, median, quaertiles, percentiles

Known distribution laws

Binomial distribution, Poisson distribution, normal distribution, standardized normal distribution

Functions of random variables

Definition of a function of random variable, determining the distribution function of functions of random variables, using the pocket calculator RND function to simulate various probability distributions

Random vector

Simultaneous distribution of a random vector,discrete random vector, simultaneous probability function, continuous random vector, simultaneous density function, marginal distributions, marginal probability functions and densities, independent random variables, correlation coefficient

Advanced distributions

Chi-squared distribution, Student's t-distribution, Fisher-Snedecor distribution