A winemaker is interested in the mean number of wine bottle (sales) at tasting events. He feels that the number of wine bottles sold has mean and that is either 8, 10, 12. The winemaker assesses the prior probabilities of P(u 8) = 0.3, P(u= 10) = 0.60, P(= 12) = 0.1. From past experience, he is willing to assume that the process has some variance given by the process. He randomly selects five tasting events and counts his number of sales he might sell, with the following results: 15, 2, 8, 10, and 7. (a) Find the winemaker's posterior distribution. (b) Compute the means and the variances of the prior and posterior distributions.