The Moment Problem is a mathematical challenge that involves determining a probability distribution based on its moments. Moments are statistical measures that provide information about the shape and characteristics of a distribution, such as its mean and variance. The problem arises when trying to find a distribution that matches a given set of moments, which can be either finite or infinite. There are two main types of the Moment Problem: the Hamburger Moment Problem and the Stieltjes Moment Problem. The Hamburger Moment Problem deals with distributions defined on the entire real line, while the Stieltjes Moment Problem focuses on distributions defined on a semi-infinite interval. Solving these problems is crucial in various fields, including statistics and physics.