15.1 We will use the Minitab macro WarICPrnac or the equivalent R function to find the posterior distribution of the standard deviation (T when we have a random sample of size n from a norma@, u2) distribution and the mean p is known. We have Sx an inverse chi-squared(&) prior for the variance u2. This is the conjugate family for normal observations with known mean. Starting with one member of the family as the prior distribution, we will get another member of the family as the posterior distribution. The simple updating rules are S'=S+SST and d=&+n, where SST = C(yi - p)’. Suppose we have five observations from a norrnal(p, u2) distribution where p = 200 is known. They are:

206.4 197.4 212.7 208.5 203.4

(a) Suppose we start with a positive uniform prior for the standard deviation

(b) Find the posterior using the Minitab macro NKarlCPrnac or the equivalent

(c) Find the posterior mean and median.

(d) Find a 95% Bayesian credible interval for u.

u. What value of S x an inverse chi-squared( 6) will we use?

R function.