Consider the following classication problem. Suppose that X is an observation from the

density

p(xj) = exp(-(x - ))I( < x < 1);

where I(:) denotes the indicator function and the parameter space is = (1; 2; 3). It is

desired to classify X as arising from p(xj|1), p(xj|2), or p(xj|3), under a 0-1 loss function

(zero loss for a correct decision, a loss of one for an incorrect decision).

(a) Find the form of the Bayes rule for this problem.

(b) Find the minimax rule and the least favorable prior distribution.