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laura_a
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Homework Statement
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
Homework Equations
This is a beta distribution where m = n = [tex]\theta[/tex]
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 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
[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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