If a sample is taken from an infinite population of variance σ 2 where:
and s2 is to be an unbiased estimator of σ 2 then:
Stage 1: prove:
As must be greater than or equal to zero this will also show that:
which completes the proof.
Stage 2: Prove that s2 is an unbiased estimator of σ 2
Stage 1 proved that:
dividing by 'n=1' so that the left hand side is s2