The alias method of Walker is a clever, new, fast method for generating random variables from an arbitrary, specified discrete distribution. A simple probabilistic proof is given, in terms of mixtures ...

A random variable is one whose value is unknown or a function that assigns values to each of an experiment’s outcomes. A random variable can be discrete or continuous.

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 ...