The moment-generating function (mgf) is a mathematical function that summarizes all the moments of a probability distribution. By taking the expected value of the exponential function raised to the power of a random variable, the mgf provides a powerful tool for characterizing distributions and is particularly useful for deriving properties like the mean and variance. The mgf can also aid in finding the distribution of sums of independent random variables.
congrats on reading the definition of mgf. now let's actually learn it.