11.1 Use the Minitab macro NormDPmac to find the posterior distribution of the mean p when we have a random sample of observations from a normal (p, 02), where u2 is known, and we have a discrete prior for p.

Suppose we have a random sample of n = 10 observations from a normal

(p, u2) distribution where it is known o2 = 4. The random sample of observations are:

3.07 7.51 5.95 6.83 8.80 4.19 7.44 7.06 9.67 6.89 We only allow that there are 12 possible values for p, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, and 9.5. If we don’t favor any possible value over another, so we give all possible values of p probability equal to A. The prior distribution is: