Homework Assignment
Problem 1
The Chief Information Officer (CIO) at Polytechnic is trying to improve the College’s information network
security. The CIO is trying to evaluate a new intrusion detection technology in the market for possible
replacement for the existing system. An intrusion detection system sounds an “alarm” each time possible
malicious attack on a network is detected. The following information is provided:
• Probability of an actual malicious attack is 0.01.
• For the currently installed system, the probability of an alarm given that there is an actual malicious
attack is 0.9, while the probability of an alarm given there is not a malicious attack is 0.25.
• For the new technology, the probability of an alarm given that there is an actual malicious attack is 0.8,
while the probability of an alarm given there is not a malicious attack is 0.1.
• The CIO assumes that there are only two types of events: either there is or there is no malicious attack.
• The CIO is using “evidence ratio,” described as P(B|A) / P(B|A’) as a way to compare the technologies.
Please help the CIO compare the new technology with the currently installed system by answering the
following questions:
1. Based on the definition of evidence ratio in the previous paragraph, what is the evidence ratio for the
currently installed system?
2. What is the evidence ratio for the new technology?
3. Which technology is better? Existing technology or new technology?
Problem 2
Frodo, a junior engineer at Baggins Metal Works is considering the introduction of a new line of products. In
order to produce the new line, the company needs either a major or minor renovation of the current plant. The
market for the new line of products could be either favorable or unfavorable, each with equal chance of
occurrence. The company has the option of not developing the new product line at all.
With major renovation, the company’s payoff from a favorable market is $100,000, from an unfavorable
market, $ -90,000. Minor renovation and favorable market has a payoff of $40,000 and an unfavorable market,
$-20,000. Not developing the new product line effectively has $0 payoff.
Frodo realizes that he should get more information before making his final decision. He contracted with
Gandalf Market Research to conduct a market analysis to determine for certain if the market will be favorable
or unfavorable. How much is the maximum amount Frodo should be willing to pay for this accurate
information? (Please indicate your answer to the nearest whole number)
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?
3. What does this graph show about John’s incremental satisfaction?
4. True/False “The shape of John’s utility function shows that he is willing to accept more risk than a riskneutral person.”
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 $.
Problem 4
There are two sub-systems (1 and 2). Failure of sub-system1 will make sub-system2 35% inoperable, while
failure of sub-system2 will make sub-system1 50% inoperable
1. Matrix A can be written as:
| X1 | X2 |
| A= | X1 |
| X2 |
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 5
Apply Borda 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”?
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