Simple counterexamples to two open problems, due to PP olya and to Karlin, discussed very recently in 4], are given.

Statement of scope and purpose: Urn models are commonly used to motivate and formulate problems in discrete probability. Typically, an urn contains some number of colored balls from which the balls are drawn according to rules particular to an application. The problem is usually to characterize the probability distribution of the balls drawn or those remaining in the urn. Numerous textbooks on ...

The Friedman’s urn model is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we prove that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman’s ur...