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

  1. Aug 7, 2008 #1
    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 :)
     
    Last edited: Aug 7, 2008
  2. jcsd
  3. Aug 9, 2008 #2
    dont worry ive got it now!
     
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