 2018 - 2019 | |||||||||||||||||||||||||||||||||||
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| 0365-2100-01 | Probability for Sciences | ||||||||||||||||||||||||||||||||||
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| FACULTY OF EXACT SCIENCES | |||||||||||||||||||||||||||||||||||
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University credit hours: 4.0
Course description
- General probability spaces: probability function and Sigma-field.
- One-dimensional random variables: definition. Cumulative distribution function and its characteristics. Discrete and continuous random variables. Probability function and density function and their characteristics.
- Two-dimensional random variables: discrete and continuous random variables. Marginal and conditional probability functions. Marginal and conditional density functions. Independence.
- Expected value, variance, co-variance, correlation coefficient, conditional expected value and conditional variance. Moment generating function, characteristic function and their properties.
- Special one-dimensional distributions. Transformations of random one-dimensional and multi-dimensional variables and the distribution of a sum of random variables.
- Inequalities: Markov's inequality and Chebyshev's inequality.
- Limit theorems: convergences in probability and almost everywhere. The laws of large numbers. Convergence in distribution. The connection between the various convergences.
- The central limit theorem and its uses. The normal two-dimensional and multidimensional distribution.