Probability theory I 1000-114bRP1b
Kolmogorov axioms.
Properties of probability measures. Borel-Cantelli lemma. Conditional probability. Bayes' theorem..
Basic probabilities: classical probability, discrete probability, geometric probability.
Random variables (one- and multidimensional), their distributions. Distribution functions.
Discrete and continuous distributions. Distribution densities. Parameters of distributions: mean value, variance, covariance. Chebyshev inequality.
Independence of: events, ?-fields, random variables. Bernoulli (binomial) process.
Poisson theorem. Distrubution of sums of independent random variables.
Convergence of random variables. Laws of large numbers: weak and strong. De Moivre-Laplace theorem.
Type of course
Bibliography
Billingsley, P., Probability and Measure.
Feller, W., An introduction to probability theory and its applications. vol. I, II,
Shiryayev, A. N., Probability, New York : Springer-Verlag, 1984.
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