We will use the Minitab macro NormGCP to nd the posterior distribution of the normal mean when we have a random samples of size n of normal(μ, σ²) observations with known σ² = 2², and we have a general continuous prior for μ.

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[R:] Use the R function normdp to find the posterior distribution of the mean when we have a random sample of observations from a nor- mal(, o), where is known, and we have a discrete prior for . Suppose we have a random sample of n = 10 observations from a nor- mal(u, 2) distribution where it is known = 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 , 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 do not favor any possible value over another, so we give all possible values of probability equal to 12. The prior distribution is: g() = { .083333 for {4.0, 4.5,..., 9.0, 9.5}, otherwise. 0