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Math Help - unbiased estimator

  1. #1
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    unbiased estimator

    We have the test samples  X_{1},...,X_{n} from
     U(-\theta,\theta)
    with parameter  \theta

    Now show that  T = (3/n) (X^{2}_{1}+....+X^{2}_{n})
    is an unbiased estimator for  \theta^2

    My main problem is that I don't know which distribution this U stands for, is it the uniform distribution?

    Can someone solve this plz
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kuntah View Post
    We have the test samples  X_{1},...,X_{n} from
     U(-\theta,\theta)
    with parameter  \theta

    Now show that  T = (3/n) (X^{2}_{1}+....+X^{2}_{n})
    is an unbiased estimator for  \theta^2

    My main problem is that I don't know which distribution this U stands for, is it the uniform distribution?

    Can someone solve this plz
    You need to show that:

     E(T) = \theta^2

    There are two ways of doing this both fairly easy. The first is to write out
    the intgral and do it, the second is to remember that the expectation operator
    is linear, so:

     E(T) = \frac{3}{n} ~\sum_{i=1}^n E(x_i^2)

    RonL
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