A sales executive hears that one of his salespeople is routing half of his incoming sales to a competitor. In particular, arriving sales are known to be Poisson at rate one per hour. According to the...

A sales executive hears that one of his salespeople is routing half of his incoming sales to a competitor. In particular, arriving sales are known to be Poisson at rate one per hour. According to the report (which we view as hypothesis H=1), each second arrival is routed to the competition; thus under hypothesis 1 the interarrival density for successful sales is f(y|H=1) = yey; y 0. The alternate hypothesis (H=0) is that the rumor is false and the interarrival density for successful sales is f(y|H=0) = ey; y 0. Assume that, a priori, the hypotheses are equally likely. The executive, a recent student of stochastic processes, explores various alternatives for choosing between the hypotheses; he can only observe the times of successful sales however.