Probability-generating function
= Probability-generating function
{wiki=Probability-generating_function}
A probability-generating function (PGF) is a specific type of power series that is used to encode the probabilities of a discrete random variable. It is particularly useful in the study of probability distributions and in solving problems involving sums of independent random variables. \#\#\# Definition For a discrete random variable \\( X \\) that takes non-negative integer values (i.e.