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Math Help - A random sample X

  1. #1
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    A random sample X

    Question : A random sample X_1,X_2,X_3 ..... X_n is taken. Show that the sample mean \bar X is an unbiased estimate of the population mean \mu
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    Quote Originally Posted by zorro View Post
    Question : A random sample X_1,X_2,X_3 ..... X_n is taken. Show that the sample mean \bar X is an unbiased estimate of the population mean \mu
    You will find the proof in almost any Stats textbook and undoubtedly Google will turn up proofs in abundance. Also, see here:http://www.mathhelpforum.com/math-he...stimators.html (and no doubt using the Search tool will turn up more threads).
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    I was able to find one but dont know if its correct or no

    Quote Originally Posted by mr fantastic View Post
    You will find the proof in almost any Stats textbook and undoubtedly Google will turn up proofs in abundance. Also, see here:http://www.mathhelpforum.com/math-he...stimators.html (and no doubt using the Search tool will turn up more threads).

    Since f(x) = \frac{1}{ \sigma \sqrt{2 \pi}} . e^{- \frac{(x- \mu)^2}{2 \sigma}}

    it follows that

    ln f(x) = - ln \ \sigma \sqrt{2 \pi} - \frac{1}{2} \left( \frac{x- \mu}{\sigma} \right)^2<br />

    so that

    ..
    ..
    ....
    = \frac{\sigma^2}{n}..............Is the theorem u were talking about???
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  4. #4
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    Quote Originally Posted by zorro View Post
    Since f(x) = \frac{1}{ \sigma \sqrt{2 \pi}} . e^{- \frac{(x- \mu)^2}{2 \sigma}}

    it follows that

    ln f(x) = - ln \ \sigma \sqrt{2 \pi} - \frac{1}{2} \left( \frac{x- \mu}{\sigma} \right)^2<br />

    so that

    ..
    ..
    ....
    = \frac{\sigma^2}{n}..............Is the theorem u were talking about???
    I have no idea how you would think I was talking about anything like that. Did you click on the link in my first post? Have you done a Google search? Key words: mean unbiased estimator
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    thanks Mr fantastic ......
    i have got it now .......Thank u
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