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Basics of measure
theory, Lebesgue measure, integration in several variables, Fubini’s,
Stokes’ and Cauchy’s theorems. The normal distribution. Central
limit theorem. Random variables, variance, covariance, Kolmogorov’s
and Chebyshev’s inequalities, correlation. Laws of large numbers.
Moment generating functions. Compound distributions. Elements of
ruin theory. Random walks. Introduction to the Markov chains theory.
The simplest time-depending stochastic processes. Statistical
computing I (Excel, Wmaple, MiniTab, etc.).
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Main textbook: |
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Auxiliary
textbooks: |
I. Miller, M.
Miller,
John E. Freund's Mathematical
Statistics,
Prentice
Hall, 1999.
G. Grimmett, D.
Stirzaker,
Probability and Random
Processes,
Oxford University Press, 2001. |
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