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Math Help - Estimation ad confidence Interval Q2

  1. #1
    Like a stone-audioslave ADARSH's Avatar
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    Estimation ad confidence Interval Q2

    These questions are on behalf of Bill who needs urgent help but cant start threads/post for some reasons

    Question 1 : Suppose that

    X_1 , X_2,...X_n \color{red}--\color{black}^{iid}  N(\mu , \sigma^2)

    Consider the following estimators for
    \sigma^2 .

    S^{*2} =\sum_{i=1}^{n}(\frac{(X_i - \overline X)^2}{n}) and

    S^2 = \sum_{i=1}^{n}\frac{(X_i - \overline X)^2}{n-1}


    Calculate MSE of those estimators and discuss which one is closer to


    \sigma^2.

    HINT: If Z_1 , Z_2,...Z_n \color{red}--\color{black}^{iid}  N(0 , 1)

    than

    \sum_{i=1}^{n} (Z_i-\overline{Z})^2 \color{red}--\color{black} {\chi}^2_{n-1}



    Note: MSE - Mean squared Error

    iid = independent and identically distributed

    --
    = ~ and iid is above it
    Last edited by ADARSH; March 30th 2009 at 11:48 PM.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Estimation ad confidence Interval Q2

    The question 2 of the attachment, Can't type now , Sorry, again this is also for Bill
    Attached Thumbnails Attached Thumbnails Estimation ad confidence Interval Q2-gasd.jpg  
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  3. #3
    MHF Contributor matheagle's Avatar
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    {(n-1)S^2\over \sigma^2} is a \chi^2 random variable with n-1 degrees of freedom.

    Hence S^2 is unbiased for \sigma^2.

    The variance of a \chi^2 random variable with n-1 degrees of freedom is 2(n-1).
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  4. #4
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    Unhappy HELP with POSTED assignment (Both questions by Bill)

    Please help with both questions, I have the same problem set, and it looks Japanese to me!!!
    The Gamma one is very hard.
    Please any help!!!!
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  5. #5
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    Quote Originally Posted by polyluka15 View Post
    Please help with both questions, I have the same problem set, and it looks Japanese to me!!!
    The Gamma one is very hard.
    Please any help!!!!
    So where are you stuck? What part of matheagle's reply do you need clarification on? What have you tried?
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  6. #6
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    There is question #2 about the Gamma distribution.
    a) its a F-distribution where
    Z=(X/k) over (Y/m), but in this question I dunno what k and m are??? and even if Z is correct

    b) NO CLUE

    c) I found this:

    Estimate + - (critical value)*(standard error)

    where the critical value comes from the relevant distribution e.g. Normal, t, chi-square, F, Gamma, and so on.

    However, the standard error will vary depending on statistic being estimated.

    Of which I don't know what is what.

    Am I out of it? I have little idea of what is going on
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  7. #7
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    thats sad

    ill tell y teacher its unsolvable, none of the ta's i called in toronto, could help.
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  8. #8
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    Quote Originally Posted by polyluka15 View Post
    ill tell y teacher its unsolvable, none of the ta's i called in toronto, could help.
    This thread is relavant to question 2: http://www.mathhelpforum.com/math-he...on-ratios.html
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