It is desired to test the null hypothesis that a sequential sample has a U (0, 2)common density versus the alternative hypothesis that the common density is U(1, 3). The cost of each observation is

c, and the decision loss is "0-K" loss.

Let , denote the prior probability of H,.

(a) Show that the Bayes sequential procedure is either d₁ or d₂, where d is the procedure which makes an immediate Bayes decision, and d₂ is the procedure which starts sampling and, at stage n, is given by the following:

if x ≤1, stop sampling and accept Ho:

if x, 2, stop sampling and accept Н₁;

if 1

(b) Calculate the Bayes risks of

d, and d₂.