If S2 is the sample variance based on a sample of size n from a normal population, we know that (n - l)S2/Ï2 has a

If S2 is the sample variance based on a sample of size n from a normal population, we know that (n - l)S2/σ2 has a X2n-1 distribution. The conjugate prior for σ2 is the inverted gamma pdf, IG(α, β), given by

where α and β are positive constants. Show that the posterior distribution of σ2 is

Find the mean of this distribution, the Bayes estimator of σ2.

2)a+1 -1)S11-1