A large lot has p% defectives and you have to predict p. If you predict p correctly you gain $g, and if the prediction is wrong, you lose $l. It is known that the possible values of p are p1, p2, . . ., pk.
(a) Set up a utility table.
(b) Suppose you assume a uniform prior for p. That is π(pi) = 1/k , i = 1, 2, . . . , k. Find an expression for the Bayes decision.
(c) Suppose you have an observable X such that P (X = x1 | pi) = ai, I = 1, 2 . . ., k and P (X = x1 | pi) = 1
ai, i = 1, 2,. . ., k. Find the updated prior for p. What is the Bayes decision in this case?