Which formula do we use for the third moment about the mean? Is it (E[X^3]-3uE[X^2]+2nu^3)/n or (E[X^3]-3uE[X^2]+2u^3)/n or just E[X^3]-3uE[X^2]+2nu^3 Thanks
You seem to be mixing up sample moments (which have n's in) and the population/theoretical moments (which don't). Assuming that you are talking about the population/theoretical moments then this is given in Chapter 3 Section 3.4 as: \(E[(X-\mu)^3]\) which can be expanded to \(E(X^3) - 3\mu E(X^2) + 2\mu^3\)
It's given in Chapter 1 Section 3.2: \(\frac{1}{n} \sum\limits_1^n (x_i - \bar x}^3\) You can expand this in a similar way.
