Probability Generating Functions (PGFs) are a powerful tool in probability theory, providing an alternative way to represent discrete probability distributions. They simplify the process of calculating probabilities, and finding the expectation and variance of a probability distribution
In this blog post, I introduce two video tutorials that guide students through the basics of PGFs. The first tutorial explains how we use Probability Generating Functions, while the second applies these ideas to derive PGFs for three common distributions: Poisson, Geometric, and Binomial.
The first tutorial provides an introduction to Probability Generating Functions. It covers:
Watch the tutorial to understand how to write a probability distribution using a PGF.
The second tutorial walks through the derivation of PGFs for:
Watch the tutorial to see step-by-step derivations of these distributions.
Students learn how to create a probability generating function to describe a probability distribution.
Later, as learning progresses they use probability generating functions to find the probability of a range of events.
Students learn how to use the standard probability generating functions for discrete probability distributions.
Later, as learning progresses they prove the standard distribution formulae for Binomial, Poisson, and Geometric distributions from the first principals.
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