Characteristic Function

A characteristic function is a mathematical tool used in probability theory to uniquely describe the distribution of a random variable. Think of it as a special kind of summary that captures all the information about how a variable behaves, similar to how a fingerprint uniquely identifies a person. It transforms the distribution into a function that makes analyzing properties like averages and variances easier, especially when dealing with sums of random variables or complex distributions. Essentially, the characteristic function helps statisticians understand and work with the randomness of data in a precise, structured way.