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Math Help - Show that the sample mean is an unbiased estimator of the population

  1. #1
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    Show that the sample mean is an unbiased estimator of the population

    Show that the sample mean is an unbiased estimator of the population mean.

    i started a nw topiuc and i have been askd this. i know definition of sample mean and bias. i know unbias estimater but idont know how to show it i dont know what i plug in from puppulation mean etc
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Caption12 View Post
    Show that the sample mean is an unbiased estimator of the population mean.

    i started a nw topiuc and i have been askd this. i know definition of sample mean and bias. i know unbias estimater but idont know how to show it i dont know what i plug in from puppulation mean etc
    You need to show that the expectation of the sample mean is equal to the population mean.

    \displaystyle \overline{x}=\frac{1}{n}\sum_{i=1}^n x_i

    where the $$x_i are iid with pdf f_X(x_i)

    Therefore:

    \displaystyle E(\overline{x})=E\left(\frac{1}{n}\sum_{i=1}^n x_i \right)=\frac{1}{n}\sum_{i=1}^n E(x_i)

    etc...

    CB
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  3. #3
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    consider the unbias estimaters mu1hat = 1/2 xbar + 1/2 ybar. and mu2hates = 1/3 xbar + 2/3 ybar. calculate the variance of mu1hat and mu2hats
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  4. #4
    MHF Contributor matheagle's Avatar
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    we're back to the moo haters?
    I mean mu haters.
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