Discrete variable's values are also "disjoint," so we have the gaps in a discrete variable's probability distribution graph. While the formula for the expected value of a discrete variable may seem ...

Invariance of a random discrete distribution under size-biased permutation is equivalent to a conjunction of symmetry conditions on its finite-dimensional distributions. This is applied to ...

It includes discrete and continuous random variables, their probability distributions and analytical and statistical methods for determining the mean, variance and higher order moments that ...

This is a graduate-level course focused on techniques and models in modern discrete probability. Topics include: the first and second moment methods, martingales, concentration inequalities, branching ...

This is a graduate-level course focused on techniques and models in modern discrete probability. Topics include: the first and second moment methods, Chernoff bounds and large deviations, martingales, ...

Examples of such complex random systems come from statistical mechanics, stochastic homogenisation, machine learning and random discrete structures. Within this RTG we strive to advance (tools for) ...

Let F be a probability distribution on R. Then there exist symmetric (about zero) random variables X and Y whose sum has distribution F if and only if F has mean zero or no mean (finite or infinite).