I am studying statistics on my own. Please help me in understanding following
Here in evaluation of Expectation $E[\frac{(n-1)S^2}{\sigma^2}]$, why $\sigma^2$(population variance is treated as constant). What to consider a constant and what as variable, how to differentiate?
My thinking - We donot know population variance $\sigma^2$. So we come up with some sample and calculate its sample variance and try to see that it is closest estimate of population variance. But when we treat $\sigma^2$ as a known constant(it means already known value?), then why again are we calculating sample variance.
pardon me for the silly question.
another doubt - why in sample variance we are considering $1/(n-1)$ and in population variance $1/n$. When we take sample size n large enough ie., n tends to infinity, does n and n-1 do mean same ?
