KnowraProbability-generating functionLinked fromLinked fromThe 11 pages that link to Probability-generating function, each with the reason it gives.All 11Related 6Compared with 5Independent and identically distributed random variablesRelated: For independent integer-valued variables, the sum's generating function is the product of theirs.Laplace transformRelated: Laplace's work on probability helped establish transform methods for encoding distributions.Probability mass functionRelated: Its coefficients recover the mass function when outcomes are nonnegative integers.Bernoulli trialRelated: For a Bernoulli outcome, its generating function is 1−p+pz and helps derive repeated-trial distributions.Negative binomial distributionRelated: Its closed form yields moments and sums for the failure count.Poisson limit theoremRelated: Convergence of binomial generating functions provides a compact proof of the limit.