Urn Models and Rudiments of Discrete Probability Probability Axioms Random Variables Independence of Discrete Random Variables Realization of Basic Discrete Distributions via Urns The Poisson Process Markov Chains Exchangeability Some Classical Urn Problems Ballot Problems Occupancy Problems Coupon Collector's Problems The Gambler's Ruin Banach's Matchbox Problem Pólya Urn Models Tenability The Pólya-Eggenberger Urn Bernard Friedman's Urn The Bagchi-Pal Urn The Ehrenfest Urn Poissonization The Pólya Process Poissonization of Multicolor Deterministic Schemes The Deterministic Monochromatic Pólya Process The Pólya-Eggenberger Process The Ehrenfest Process Poissonization of Schemes with Random Entries The Depoissonization Heuristic Depoissonization of Dichromatic Pólya Processes Depoissonization of Invertible Processes Depoissonization Examples Urn Schemes with Random Replacement Martingales Extended Urn Schemes Deterministic Dichromatic Extended Urn Schemes Dichromatic Extended Urn Schemes with Random Entries Extended Multicolor Urn Schemes Analytic Urns Enumerating Histories in Balanced Schemes Analytic Urn Examples Applications of P ólya Urns in Informatics Search Trees Recursive Trees Urn Schemes in Bioscience Evolution of Species Competitive Exclusion Epidemiology: Kriz' Polytonomous Urn Scheme Clinical Trials Urns Evolving by Multiple Drawing Urns Evolving by Drawing Pairs of Balls The Chen-Wei Urn Linear Rectangular Urns Application of Rectangular Schemes in Random Circuits Answers to Exercises Notation Bibliographic Notes Bibliography Index Exercises appear at the end of each chapter. The Ehrenfest Process Poissonization of Schemes with Random Entries The Depoissonization Heuristic Depoissonization of Dichromatic Pólya Processes Depoissonization of Invertible Processes Depoissonization Examples Urn Schemes with Random Replacement Martingales Extended Urn Schemes Deterministic Dichromatic Extended Urn Schemes Dichromatic Extended Urn Schemes with Random Entries Extended Multicolor Urn Schemes Analytic Urns Enumerating Histories in Balanced Schemes Analytic Urn Examples Applications of P ólya Urns in Informatics Search Trees Recursive Trees Urn Schemes in Bioscience Evolution of Species Competitive Exclusion Epidemiology: Kriz' Polytonomous Urn Scheme Clinical Trials Urns Evolving by Multiple Drawing Urns Evolving by Drawing Pairs of Balls The Chen-Wei Urn Linear Rectangular Urns Application of Rectangular Schemes in Random Circuits Answers to Exercises Notation Bibliographic Notes Bibliography Index Exercises appear at the end of each chapter. n Epidemiology: Kriz' Polytonomous Urn Scheme Clinical Trials Urns Evolving by Multiple Drawing Urns Evolving by Drawing Pairs of Balls The Chen-Wei Urn Linear Rectangular Urns Application of Rectangular Schemes in Random Circuits Answers to Exercises Notation Bibliographic Notes Bibliography Index Exercises appear at the end of each chapter.