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Topic: Sampling From Finite Population with Replacement
Replies: 28   Last Post: Sep 30, 2010 6:30 AM

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 cagdas.ozgenc@gmail.com Posts: 58 Registered: 3/29/06
Re: Sampling From Finite Population with Replacement
Posted: Sep 29, 2010 3:03 PM

>
> >> The population mean is an unbiased estimate of the generator mean.
> >> The sample mean is an unbiased estimate of the population mean,
> >> and therefore of the generator mean.

>
> > I think you have a point here. But as you can see that there is a
> > problem with consistency.

>
> > Let's say that generator mean is Mu, and population mean is Mu + Eps.
> > And I take as you suggest Eps is a random error not a systematic error
> > (not a bias).

>
> > Now as you take more and more sample means, you will see that they
> > will start to gather around Mu+Eps not Mu. Now do we have a random
> > error or a systematic error?

>
> It all depends on whether we're talking about the conditional
> distribution of the sample mean, given the population mean; or the
> unconditional (or marginal) distribution of the sample mean. As an
> estimate of the generator mean, the ssmple mean is conditionally
> biased but marginally unbiased.
>

I don't think I am following you. How is all that related to
conditioning?