moment generating function

A moment generating function (MGF) is a mathematical tool used to describe the probability distribution of a random variable. It encodes all the moments (like the mean and variance) of the distribution into a single function. By analyzing the MGF, statisticians can easily find the expected value, variability, and other characteristics of the data. Essentially, it’s a compact way to capture the entire behavior of a random variable, making it easier to compare different distributions and analyze their properties in a systematic way.