The failure of a circuit board interrupts work that utilizes a computing system until a new board is delivered. The delivery time, Y, is uniformly distributed on the interval one to five days. The cost of a board failure and interruption includes the fixed cost c0 of a new board and a cost that increases proportionally to Y2. If C is the cost incurred, C=c0+c1Y2. a) Find the probability that the delivery time exceeds two days.
b) In terms of c0 and c1, find the expected cost associated with a single failed circuit board.