Q. 3 MAP for disk failure At a computer disk drive factory, inspectors randomly pick a product from production lines to detect a failure. If the production lines are normal, this failure rate q0 = 10 . However occasionally some problems occur in the lines, in which case the rate goes up to q1 = 10-2. Let H; denote the hypothesis that the failure rate is qi- Every morning, an inspector chooses drives at random from the previous day's production and tests them. If a failure occurs too soon, the company stops production and checks the critical part of the process. Produc- tion line problems occur about once every 10 days, so we will say P(H1 ) = 0.1 =1 - P(Ho). 1. Based on /, the number of drives tested up to and including the first failure, design a MAP test that will use / to determine which hypothesis is true. 2. Calculate the probability of 'false alarm' (i.e. our MAP test computed in previous part concludes that the rate is q wrongly) and the probability of 'missed detection' (i.e. our MAP test fails on detect that the rate is q1). 3. Based on this, calculate the probability of detection error PE