Suppose our prior belief is is just as likely to be below 8 as it is

Suppose our prior belief is σ is just as likely to be below 8 as it is to be above 8. (Our prior distribution g(σ) has median 8.) Determine an S x an inverse chi-squared(k) that matches our prior median where we use k = 1 degree of freedom.

(a) Find the posterior using the macro NVarICP in Minitab or the function nvaricp in R.
(b) Find the posterior mean and median.
(c) Find a 95% Bayesian credible interval for σ.