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?


No, I think it's correct both times.
That the sum goes from 0 is clear from the binomial expansion. That the comment about what you're writing it in terms of is nevertheless correct  can be seen by expanding it out and seeing that the final term involves constants ($\mu_0$ is just $1$) and a power of $\mu_1$; note that the last and second-last terms both only have $\mu_1$.
