Problem 1

There are two sub-systems (1 and 2). Failure of sub-systeml will make sub-system2 35% inoperable, while failure of sub-system2 will make sub-systeml 50% inoperable

1. Matrix A can be written as:

Suppose that sub-system2 is attacked with intensity h = 90%. Using matrix equation x = Ax + c, where x is the inoperability of the sub-systems, A is the dependency matrix, and c is the intensity of attack, please match the values to the following questions

2. What is the resulting value of x₁?

3. What is the resulting value of x₂?

Problem 2

Apply Gorda algorithm to score and rank the risk events shown.

1. What is the score of "Telephone"?

2. What is the score of "Cellular"?

3. What is the score of "Cable"?

Problem 3

John Doe is a rational person whose satisfaction or preference for various amounts of money can be expressed as a function U(x) = (x/100)^2, where x is in $.

1. How much satisfaction does $20 bring to John?

If we limit the range of U(x) between 0 and 1.0, then we can use this function to represent John's utility (i.e. U(x) becomes his utility function).

2. What is the shape of his utility function?

CI Concave

m  Convex

m  Straight line

q  None of these

3. What does this graph show about John's incremental satisfaction?

q  Increases with increasing x

q  Decreases with increasing x

q  Does not change with k

m  None of these

4. "The shape of John's utility function shows that he is willing to accept more risk than a risk-neutral person."

 True

 False

5. John is considering a lottery which payoff $80 forty percent of the time, and $10 sixty percent of the time. If John plays this lottery repeatedly, how much will be his long-term average satisfaction?

6. For John, what certain amount would give him satisfaction equal to this lottery? Express your answer to nearest whole $.