Finding measure of skewness for binomial distribution Here's how it was done in my class: $E[(X)_3]= n(n-1)(n-2) p^3$ (Calculated using definition. I understand that part properly.) $E[(X)_2]= n(n-1)p^2$ (Calculated using definition again). Now, here's my first doubt. In the next step, it's written: $\mu_2' =E(X^2)= E[(X)_2]+E[(X)_1]= n(n-1)p^2 +np $ But isn't $\mu_2'=E[(X_2)]$, the 2nd order RAW moment? And isn't $\mu_2= E[(X^2)]$, the 2nd order CENTRAL moment? I have the same confusion regarding $\mu_3'$ too. Please help.

Your confusion stems from a misunderstanding of what "raw" and "central" moment refer to: a raw moment is $$\mathrm{E}[X^k],$$ whereas a central moment is $$\mathrm{E}[(X-\mathrm{E}[X])^k],$$ where "central" refers to having the expectation _centered_ about the mean. The quantity you write $$\mathrm{E}[(X)_k] = \mathrm{E}[X(X-1)\ldots(X-k+1)]$$ is more familiarly known as the "factorial" moment.