Part 1: Moments Definition 1 For each integer $n$, the nth moment of $X$, $\mu_n^{'}$ is \[\mu_{n}^{'} = EX^n.\] The nth central moment of $X$, $\mu_n$, is \[ \mu_n = E(X-\mu)^n,\] where $\mu=\mu_{1}^{'}=EX$. Definition 2 The variance of a random var