**Property 3**: The sample variance is an unbiased estimator of the population variance

Proof: If we repeatedly take a sample {*x _{1},…,x_{n}*} of size

*n*from a population with mean

*μ*, then the variance

*s*

^{2}of the sample is a random variable defined by

it follows that

by Property 1 of Expectation we now have

By Property 2 of Estimators

Putting all the pieces together we get

Dear Charles,

sorry, I’ve got another question…

I do not understand how do we formally move from the definition of the variance sigma^2 = E[(x-µ)^2] to the one you’re using i nthe demo sigma^2 = sum(E[(x_i – µ)^2]).

Thanks in advance,

Gilles

Dear Gilles,

What was written on the referenced webpage was a typing mistake: sigma^2 = E[(x-µ)^2] without the sum. I have now corrected this mistake on the webpage. Thanks for catching the error.

Charles