Abstract:This work is devoted to the analysis of the area under certain lattice paths. The lattice paths of interest are associated to a class of 2 × 2 triangular Pólya-Eggenberger urn models with ball replacement matrix M = −a 0 c −d , with a, d ∈ N and c = p · a, p ∈ N 0 . We study the random variable counting the area under sample paths associated to these urn models, where we obtain a precise recursive description of its integer moments. This description allows us to derive exact formulae for the expectation and th… Show more
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.