2019 - 2020

0365-2100   Probability for Sciences                                                                             
FACULTY OF EXACT SCIENCES
View groups
 
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.

accessibility declaration


tel aviv university