Biased and un-biased estimators.


New Member
I am working with the Rayleigh-distribution and note that on Wikipedia they say that
s^2 = 1/(2N) sum x_i^2
is an unbiased estimator of sigma^2. Now they also say that
s = sqrt(s^2)
is a biased estimator of sigma.

How can this be?? If one is unbiased, why isn't the other one? I mean, you have only taken the sqrt on both sides of the equation.

Thanks for any comments!