Suppose that a failure in a certain electronic system can occur because of either a minor or a major defect. Suppose also that 80 percent of the failures are caused by minor defects, and 20 percent of the failures are caused by major defects. When a failure occurs, n independent soundings X1, . . . , Xn are made on the system. If the failure was caused by a minor defect, these soundings form a random sample from the Poisson distribution with mean 3. If the failure was caused by a major defect, these soundings form a random sample from a Poisson distribution for which the mean is 7. The cost of deciding that the failure was caused by a major defect when it was actually caused by a minor defect is $400. The cost of deciding that the failure was caused by a minor defect when it was actually caused by a major defect is $2500. The cost of choosing a correct decision is 0. For a given set of observed values of X1, . . . , Xn, which decision minimizes the expected cost?