Finding the Method of moments estimator? Having trouble finding E(Y^2)

[laura_a]

Homework Statement

Let Y1, Y2, ... Yn be a random sample from the distribution with pdf
\frac{\Gamma(2 \theta)}{[\Gamma(\theta)]^2} (y^{\theta -1)(1-y)^{\theta -1}
for 0 \leq y \leq 1

I have to find the MME for theta

Homework Equations

This is a beta distribution where m = n = \theta

The Attempt at a Solution

Now I believe that E(Y) = \frac{m}{m+n}

So I worked out that E(X) = 1/2 which means it doesn't depend on theta.

SO I need to find E(Y^2) which I already know is
\frac {\theta + 1}{2(2 \theta +1)}

but I just don't know how to get it. I must be missing a formula because if I just do E(Y^2) from what I have, I end up with

\frac{1}{4}

I can't even begin to find the MME because I can't find E(Y^2)

Can anyone suggest a path I should go down? Thanks :)

 

[laura_a]

dont worry I've got it now!