1. The US Federal Motor Carrier Safety Administration
planned in 2013 to issue rules that would limit the number of hours per week
that truck drivers can work. The rules would reduce driver workweeks (fewer
hours), restrict the number of nights that truckers can work, and require rest
breaks during the day. The impacts could include keeping sleep deprived drivers
off the road, reducing crashes, preventing fatigue-related crashes, improving
working conditions, reducing driver turnover, improving driver safety, saving
lives, reducing injuries, and reducing fatigue-related health problems.
a. Identify 3 risks associated with
this information
b. Using the risk/opportunity
approach, develop a conceptual model including events, triggers, mitigation,
control and consequences
2. There are three identical and independent temperature
sensors that will trigger in:
90% of the cases where the
temperature is high
5% of the cases where the
temperature is nominal
1% of the cases where the
temperature is low.
The probability of high temperature is 20%, nominal
temperature is 70%, and low temperature is 10%. Describe a Bayesian network and
corresponding queries for computing the following:
(a) Probability that the first
sensor will trigger given that the other two sensors have also triggered
(b) Probability that the
temperature is high given that all three sensors have triggered
(c) Probability that the
temperature is high given that at least one sensor has triggered
3. A few weeks after inseminating a cow, we have three
possible tests to confirm pregnancy. The first is a scanning test (S) that has
a false positive of 1% and a false negative of 10%. The second is a blood test
(B) that detects progesterone with a false positive of 10% and a false negative
of 30%. The third test is a urine test (U) that also detects progesterone with
a false positive of 10% and a false negative of 20%. The probability of a
detectable progesterone level is 90% given pregnancy and 1% given no pregnancy.
The probability that insemination will impregnate a cow is 87%. Suppose now
that we inseminate a cow, wait for a few weeks, and then perform the three
tests, which all come out negative. Using a Bayesian model determine the
probability that the cow is pregnant?
4. A manufacturing firm has signed a contract to produce a
product to demand, receiving $500 per unit. The firm could either produce the
product itself or outsource the production. Demand is exponentially distributed
with a mean of 10,000 units per year. In-house production has
normally-distributed fixed costs with mean of $500,000 and a standard deviation
of $100,000 and normally-distributed variable costs with mean $200 and standard
deviation of $10. Outsourcing has no fixed cost, but variable costs are $250.
a. Create a diagram for this problem b. Forecast the profit for each alternative
c. Determine the difference in profit d. Determine the probability that each
alternative achieves at least $0 profit, $100,000 profit, and $200,000 profit
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