Probability Theory and Mathematical Statistics

The course introduces fundamentals of the probability theory and mathematical statistics and illustrates these concepts with engineering applications. The course covers basic principles of probability calculus (classical probability, conditional probability and the Bayes rule, Bernoulli trials), deep introduction into random variables (uniform, binomial, geometric, Poisson, exponential, normal, and several statistical distributions), probability limit theorems (Bernoulli and Chebyshev law of large numbers, Poisson and central limit theorems) and selected topics of mathematical statistics (sampling, point and interval estimates, statistical hypothesis testing, correlation). The course supplements deep theoretical concepts with practical computer-based exercises (R language).