Variance of Discrete Random Variable from PGF/Motivation
Variance of Discrete Random Variable from PGF: Also known as
Variance of Discrete Random Variable from PGF shows how to find the variance of a discrete random variable without the need to go through the tedious process of what might be a complicated and fiddly summation.
All you need to do is differentiate its PGF twice, and plug in $1$.
Assuming, of course, you know what its PGF is.