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(civl581)[2000](s)midterm~PPSpider^_10082.pdf
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Name:
Prof. Tang
Apr. 1, 2000
CIVL 581 Midterm Examination
Problem 1 (20%)
Circle T (true) or F (false) for each of the following statements. A correct answer will score 2 points; whereas one point will be deducted for each incorrect answer.
T F
A good engineer should eliminate all uncertainties before adopting a design.
T F
If two events are statistically independent, they can be still mutually exclusive.
T F
Even if two engineers disagree on the probability value of a given event in a decision tree, they may still end up selecting the same alternative.
T F
If the probability of a fire occurring in Sai Kung in a given month is 0.1, the return period of fire in Sai Kung is 10 years.
T F
In the Weighted Objective Decision analysis, the relative weights between objectives are generally determined from judgmental information by using tools such as ordinal and cardinal ranking.
T F
Value of perfect information for a given decision problem is generally smaller for a risk aversive person than one who is risk indifferent.
T F
Utility of an event can take on negative values.
T F
For a risk aversive person, the choice of an alternative is more appropriate using the Expected Monetary Value (EMV) criteria than the Expected Utility Value (EUV) criteria.
T F
In the determination of a utility function for money, the utility of $1000 and $100 may be assigned the utility values of 3 and 8 respectively.
T F
The sum of three lognormal random variables is a lognormal random variable itself.
Problem 2 (40%)
For a certain type of dangerous construction project, the time T (in days) elapsed between two successive accidents follows an exponential distribution,
fT(t) = eCt (t 0)
where the parameter depends on site conditions. It is believed that could be either 1/5 or 1/10 with relative likelihood 1:2. For a particular site, accidents were reported on days 2 and 5 from the commencement date of the project, respectively.
(a)
What is the updated probability that is 1/10? (Hint: please note that we do not know if any accident took place just before the project commencement date)
(b)
What is the probability that no accidents will occur for at least 10 days after the second accident?
(c)
Suppose, after the second accident, the construction projected has entered its 15th day from commencement without having a third accident. What is the probability that is 1/10 now?
(d)
For the next 10 days of construction (i.e. between day 15 and day 25), if the number of accidents exceeds a certain number (nC), then one would be more inclined towards the belief that is 1/5 than its being 1/10. Determine this critical number nC.
(e)
Rather than the discrete values 1/5 a