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 1 to 5 days. The cost incurred following a board failure is related to the delivery time for a new board by the formula C = 50 + 3Y + 9Y2. The E(C), the expected cost associated with the failure of a circuit board is.

The expected cost is 152

Step-by-step explanation:

Recall that since Y is uniformly distributed over the interval [1,5] we have the following probability density function for Y

if and 0 othewise. (To check this is the pdf, check the definition of an uniform random variable)

Recall that, by definition  

Also, we are given that . Recall the following properties of the expected value. If X,Y are random variables, then

Then, using this property we have that .

Thus, we must calculate E[Y] and E[Y^2].

Using the definition, we get that

Then

the correct answer is $7.38

step-by-step explanation: