Q&A Part 3- question 12

[shana]

Hi
can anyone explain the calculation behind Skew(s)?
cant seem to understand how the got there?

 

[peace]

This is a compound poisson distribution, where Skew(S) = λ * E (X^3)

To find the value of E (X^3), follow similar steps to that of calculating E(X^2), except that use the following skewness formula.

Skewness of X = E[(X -E(X))^3] = E(X^3) -3*E(X)* E(X^2) + 2*E^3(X )

We are given: (working in millions of dollars )
Mean of X = E(X) = 5;
Variance of X = 3^2 ( Hence E(X^2) = Var (X) +E^2(X) = 3^2 + 5^2 = 34 )
Skewness of X = 4^3

Substituting above values in the equation for skewness.
4^3 = E(X^3) – (3*5*34) + 2*5^3
Hence E(X^3) = 4^3 + (3*5*34) - 2*5^3 = 64 + 510 -250 = 324

Now, Skewness of S = λ * E (X^3) = 2 * 324 = 648 ( where λ = 2 given)

 

[shana]

Thanks..

for some reason I thought Skewness was calc by:
{E(x-E(X))^3}/(STDV(X)^3)
I guess not...
Thanks and goodluck