It is desired to test the null hypothesis that a sequential sample has a common density versus the alternative hypothesis that the common density is The cost of each observation is c, and the...

It is desired to test the null hypothesis that a sequential sample has a

common density versus the alternative hypothesis that the common density is

The cost of each observation is c, and the decision loss is

loss. Let

denote the prior probability of

(a) Show that the Bayes sequential procedure is either dl or d₂, where dl 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:

(b) Calculate the Bayes risks of d₁, and d₂