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!