This paper contains inequalities for the expectations of permutation-invariant concave functions and Schur-concave functions of the partial sums of nonnegative exchangeable random variables. Two ...

Characteristic and generating functions. Vector formulation of random variables and their parameters. Mean square estimation and orthogonality principle. Criteria for estimators. Introduction to ...

P. Scheinok, The Distribution Functions of Random Variables in Arithmetic Domains Modulo a, The American Mathematical Monthly, Vol. 72, No. 2 (Feb., 1965), pp. 128-134 ...

Functions of Random Variables. Monte Carlo Simulation in R. Joint distributions and joint moments. Marginal and conditional densities. Independence, covariance and correlation. Sums of random ...

Introduction to the theories of probability and random variables, and their applications in the analysis and modelling of engineering systems. Topics include: a review of probability and random ...

Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws ...

The course covers the probability, distribution theory and statistical inference needed for third year courses in statistics and econometrics. Michaelmas term: Events and their probabilities. Random ...

In the first part, participants will get to learn the following modules: Introduction to data science, basic calculations with R Software and probability theory, probability theory and random ...