You've been asked to test the performance of a batch of newly fabricated processors. if theprocessors were correctly manufactured (class y = 0), the time x to complete your test suiteis exponentially distributed with mean 1. if the equipment at the factory malfunctions (classy = 1), the time x is exponentially distributed with mean 50. you must decide whether ornot this batch of processors was correctly manufactured. a) suppose that a new fabrication process has just been deployed, and the probability thatthe factory manufactures correctly functioning processors is only p(y = 0) = 0.5. asa function of the observed test suite time x = x, what classifcation rule maximizes theprobability that your prediction is correct? b) suppose that after some improvements to the new fabrication process, the probability thatthe factory manufactures correctly functioning processors increases to p(y = 0) = 0.99.as a function of the observed test suite time x = x, what classifcation rule maximizesthe probability that your prediction is correct?