1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook