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Probability and Statistics

Included:

  • Elements of combinatorics.
  • Probability of random events.
  • Independence of random events.
  • Random vectors: marginal and conditional distributions.
  • Functions of random variables.
  • Numerical properties of random variables: mathematical expectation, variance of a random variable, correlation coefficient between two random variables.
  • Central border theorem.
  • Elements of statistics: population and sample, parameters and statistics.
  • Basic data processing and descriptive statistics.
  • Sample statistics distributions: normal, t-distribution, Chi-square and F-distribution.
  • Evaluation of landmark parameters: method of moments, method of maximum suitability, confidence intervals.
  • Parameter tests.
  • Nonparametric tests.
  • Linear regression, estimation by the least squares method.m events.
  • Properties of probabilities.
  • Discrete probability space.
  • Conditional probability.