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Math Help - How to find the variance

  1. #1
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    How to find the variance

    Hi,

    I apologize in advance for the crappy title but I didn't know how else to describe my problem. I'm trying to solve a problem where Y1, Y2, ... , Yn is a random sample of size n from a normal population with mean = (mu) and variance = (sigma^2).

    We are given an estimator for (sigma^2):
    (sigma^2) = 1/2k [summation from i=1 to k] (Y2i - Y2i-1)^2
    where 2i and 2i-1 above are subscripts of the Y's.

    I'm trying to show that the estimator above is consistent using the variance. I know that the mean of each term [(Y2i - Y2i-1)^2]/2 has mean of (sigma^2) but it says in the solution that the variance of each such term is 2(sigma^4) and I can't figure out how they get that.

    Any ideas?

    Thanks...
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  2. #2
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    Quote Originally Posted by Canadian0469 View Post
    Hi,

    I apologize in advance for the crappy title but I didn't know how else to describe my problem. I'm trying to solve a problem where Y1, Y2, ... , Yn is a random sample of size n from a normal population with mean = (mu) and variance = (sigma^2).

    We are given an estimator for (sigma^2):
    (sigma^2) = 1/2k [summation from i=1 to k] (Y2i - Y2i-1)^2
    where 2i and 2i-1 above are subscripts of the Y's.

    I'm trying to show that the estimator above is consistent using the variance. I know that the mean of each term [(Y2i - Y2i-1)^2]/2 has mean of (sigma^2) but it says in the solution that the variance of each such term is 2(sigma^4) and I can't figure out how they get that.

    Any ideas?

    Thanks...
    Read this thread: http://www.mathhelpforum.com/math-he...estimator.html
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  3. #3
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    Sweet! Thanks. I really don't know how you found that.
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