Probability

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Department of Applied Mathematics

Synopsis:

Descriptive statistics: introduction to the basic problems of statistics, organizing data, graphical methods of data presentation, numerical presentation of data, measures of location or central tendency. Basic probability concepts: elementary events and events, definitions and interpretation of probability, axioms of probability theory, probability properties, conditional probability and independence, Bayes theorem. Random variable, probability distribution, probability mass and density, moments, some discrete and continuous distributions. Approximations of distributions, independence of variables. Random vectors: joint and marginal distributions, mean vector, covariance matrix. Mixed distributions, mixture of distributions. Law of large numbers, Central limit theorem.

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The course is a part of the following study plans: