Use the fact that
which comes from integration by parts
Hence
Now do it when m=2.
Given pdf is for
a) Compute the moments about the origin
b) Find the method of moments estimators for a and b (Using a sample of size n).
Attempt:
a)
b) Am i supposed to use part a to find the first and second central moments? I am not sure how to do this. Even so, by looking them up I try the following:
where m1 and m2 are the sample moments.
Basically when I try to solve this system of equations I get gross quadratics that I don't know how to simplify. Is there an elegant way of solving these, or if not, what is the best strategy for attacking these?
Ah, I did not know that fact. Thank you.
I'm still clueless on solving for the MME though.
From
I've got that
and
From
Assuming I did all my algebra right, I get
How should I approach this to get it simplified? I suppose this may belong in an algebra section.