Probability theory in tasks. Tutorial. Borzykh D.A.

The manual is intended for conducting practical classes at the “Probability Theory” course for students of economic specialties. It can also be used in the independent study of the subject due to a very large number of details solved problems.

The proposed manual contains the tasks of various levels of complexity. However, the main emphasis is on the tasks of medium complexity. This was done intentionally in order to encourage students to independently solve problems: it is boring to solve too simple problems; too complicated - demotivate medium and weak students, and strong students often take away an unjustifiably large amount of time, which, in the context of the real educational process, they do not have. Currently, it is read to the Higher School of Economics at the Faculty of Economic Sciences: basic information about discrete random values; The main discrete distributions are Bernoulli distribution, binomial distribution, Poisson distribution, geometric distribution; Conditional probability, formula for multiplication of probabilities, a formula of complete probability, the Bayes formula; Absolutely continuous random values; The main absolutely continuous distributions are uniform distribution, normal distribution, indicative (exponential) distribution; central maximum theorem, inequality of Berry Estate; Absolutely continuous random vectors.

In additions 1 and 2 manuals, tasks (with decisions) related to more complex topics are considered: the properties of a probabilistic measure; convergence by probability and distribution.