Función característíca

A función característica (or characteristic function) is a mathematical tool that uniquely describes a probability distribution by using a complex-valued function. Think of it as a special "signature" that captures all the information about a random variable’s behavior, much like a fingerprint. It helps in analyzing and understanding the properties of the distribution, especially when dealing with sums of independent variables, convergence, or transformations. The characteristic function is particularly useful because it simplifies calculations and provides a powerful way to study the distribution without needing to directly work with the probability density or mass functions.