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

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

asdsad

step-by-step explanation: