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 six 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.

a) 1  ( 100% )

b)   Co + 46/3 C1

Step-by-step explanation:

Delivery time = Y

Interval = 2 to 6 days

cost incurred ( C ) = Co + C1 Y^2

a) determine the probability that the delivery time exceeds two days

since the delivery time is uniformly distributed on the interval 2 to 6 days the probability of having a delivery time > 2 days will be = 1

b) Determine the expected cost associated with a single failed circuit board

E ( Y^2 ) = 46/3

hence the cost associated with a single failed circuit board =

E ( C ) = Co + 46/3 C1

attached below is a detailed solution

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true