Hi there, In the ques no. 4.22, it has been told to determine the third "non-central" moment of the normal distribution. However, in the solution skewness has been calculated. Why so? Skewness is supposed to be the third "central" moment. Is the solution given wrong. Someone please clarify. Thanks.
Hi ! Yes, the 3rd non-central moment is E(X^3). To compute this directly will require complex integration work. Instead you can use a standard (and very useful) result for Normal distributions. For any Normal distribution, its skewness ie 3rd central moment is 0 Using this fact and rearranging terms you can directly compute E(X^3). [0 = Skewness = E(X^3) - 3 mu E(X^2) + 2 mu^3]
