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 + c1Y 2.
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.