(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let Y1, Y2, ... Yn be a random sample from the distribution with pdf

[tex] \frac{\Gamma(2 \theta)}{[\Gamma(\theta)]^2} (y^{\theta -1)(1-y)^{\theta -1}[/tex]

for [tex] 0 \leq y \leq 1 [/tex]

I have to find the MME for theta

2. Relevant equations

This is a beta distribution where m = n = [tex]\theta[/tex]

3. The attempt at a solution

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

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

SO I need to find [tex] E(Y^2) [/tex] which I already know is

[tex] \frac {\theta + 1}{2(2 \theta +1)} [/tex]

but I just dont 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

[tex] \frac{1}{4} [/tex]

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

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

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

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