Question

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 two to seven days. The cost of a board failure and interruption includes the fixed cost Co of a new board and a cost that increases proportionally to Y2. If C is the cost incurred, C = Co + CZY. (a) Find the probability that the delivery time exceeds four days. X Enter a number. (b) In terms of c, and c,, find the expected cost associated with a single failed circuit board.

Answer 1

(a)

Y ~ Uniform(a = 2, b = 7)

Probability that the delivery time exceeds four days = P(Y > 4)

= (7 - 4) / (7 - 2) { P(Y > y) = (b - y) / (b - a) }

= 0.6

(b)

Expected cost = E(C) =

Now,

E[Y] = (a + b)/2 = (7 + 2)/2 = 4.5

Expected cost is,