For an infinite population with finite 2 , show that the sample standard deviation S is a biased estimator for s Find an unbiased estimator of We have seen that S 2 is an unbiased estimator of 2 From this exercise, we see that a function of an unbiased estimator need not be an unbiased estimator ...

For an infinite population with finite 2 , show that the sample standard deviation S is

Question:

For an infinite population with finite σ², show that the sample standard deviation S is a biased estimator for s. Find an unbiased estimator of σ. [We have seen that S² is an unbiased estimator of σ². From this exercise, we see that a function of an unbiased estimator need not be an unbiased estimator.]