Calculating E(X^3)

I am looking at the Q&A bank question 3.12 in ST8 which asks to find the skew(S). We are given E(X) and var(X) and E(N) and var(N). I know that:

skew (S) = E(N) * E(X^3) but I don't know how to calculate E(X^3) using the above information. Would you be able to help me with this please?

Thanks,

Ramiz

 

Can you calculate Skew(X) and get E(x^3)=Skew(X)-E^3(X)?

 

Is that right? I thought that

skew(x) = E(X^3) - 3E(X)var(X) - E^3(X)

? (Expand skew(X) = E[(X-µ)^3] )

Alternatively, you could use moment generating functions to get E(X^3) directly.

 

Quite right. Shows you how often I use skew in the day job!

Also worth pointing out need to take care whether we're talking about standardised skew or not...