Hi, I'm working on the following problem and I need some clarification:(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that a sample is drawn from a [tex]N(\mu,\sigma^2)[/tex] distribution. Recall that [tex]\frac{(n-1)S^2}{\sigma^2}[/tex] has a [tex]\chi^2[/tex] distribution. Use theorem 3.3.1 to determine an unbiased estimator of [tex]\sigma[/tex]

Thoerem 3.3.1 states:

Let X have a [tex]\chi^2(r)[/tex] distribution. If [tex] k>-\frac{r}{2}[/tex] then [tex]E(X^k)[/tex] exists and is given by:

[tex] E(X^k)=\frac{2^k(\Gamma(\frac{r}{2}+k))}{\Gamma(\frac{r}{2})}[/tex]

My understanding is this:

The unbiased estimator equals exactly what it's estimating, so [tex]E(\frac{(n-1)S^2}{\sigma^2})[/tex]is supposed to be[tex]\sigma^2[/tex] which is 2(n-1).

Am I going the right way here?

CC

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# Unbiased estimator

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