Possible typo in discussion of moments of a random variable I'm struggling to understand some notation in this excerpt from Larsen & Marx. Under "Comment" j is defined as 1, 2,...,r, but the sigma shows the lower bound of j as 0. Is this inconsistency a typo?


Check for yourself:
\begin{align}\mu_r' &:=\mathbb E[(W-\mu)^r]\\ &=\mathbb E\left[W^r-{{r}\choose{ 1}}W^{r-1}\mu^1 + {{r}\choose{ 2}}W^{r-2}\mu^2 - \cdots + (-1)^r\mu^r\right]  \\ &= \mu_r -{{r}\choose{ 1}}\mu_{r-1}\mu^1 + {{r}\choose{ 2}}\mu_{r-2}\mu^2  - \cdots + (-1)^r\mu^r.\end{align}
