A study on Discrete Probability Distributions using URN Models

Abstract

Probability theory, a cornerstone of statistics, provides a mathematical framework to quantify uncertainty. Within this realm, discrete probability distributions occupy a significant position, modeling random variables that can assume only a countable number of values. A particularly intuitive approach to understanding and analyzing these distributions involves the use of urn models. An urn model is a simple, yet powerful, probabilistic model that involves drawing objects from an urn. By varying the number of objects, their types, and the drawing process, we can simulate a wide range of discrete probability distributions. This approach not only enhances our comprehension of these distributions but also provides a practical tool for solving real-world problems. Bernoulli distributions, named after the Swiss mathematician Jacob Bernoulli, are fundamental in probability theory. They describe the outcome of a single experiment with two possible results: success (denoted by 1) or failure (denoted by 0). Urn models, on the other hand, provide a visual and intuitive way to understand probability concepts, including Bernoulli distributions.