Moment generating functions

Moment generating functions (MGFs) are mathematical tools used to summarize all the moments (like average, variance, skewness) of a probability distribution in a single function. By plugging in different values into this function, you can retrieve information about the distribution’s shape and characteristics. Essentially, MGFs serve as a compact way to analyze and understand the behavior of random variables, making them useful in fields like statistics and probability theory to study and compare different distributions efficiently.