What is the expected value and the mean of sample standard deviation?

I know that I can derive the expectation and variance of sample variance using the $chi^2$ pdf. But I don't know how to start with sample standard deviation.

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#### Best Answer

If the sample is IID normal then the answer is

$$ sqrt{ frac{2 sigma^2}{n-1} } times frac{ Gamma(n/2) }{ Gamma( frac{n-1}{2} ) } $$

where $sigma^2$ is the population variance and $n$ is the sample size. For a full derivation read this.

Also, mean and expected value are the same thing.

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