Statistics - Moment Generating Functions

[little neutrino]

If the moment generating function for the random variable X is M[X(t)] = 1/(1+t), what is the third moment of X about the point x = 2? The general formula only states how to find moments about x = 0. Thanks!

 

[andrewkirk]

The n-th moment of X about a is defined as $E[(X-a)^n]$.

Substitute n=3 and a=2 into that, then expand $(X-a)^n$ to polynomial form and substitute that into the above expression. You will get the sum of a bunch of moments about zero, which you can then use the MGF to calculate.

 

[little neutrino]

The n-th moment of X about a is defined as $E[(X-a)^n]$.

Substitute n=3 and a=2 into that, then expand $(X-a)^n$ to polynomial form and substitute that into the above expression. You will get the sum of a bunch of moments about zero, which you can then use the MGF to calculate.

Ok I got it! Thanks so much! :)