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Question: In the oil-wildcatting problem, suppose that the company could collect information from a drilling core sample and analyze it to determine whether a dome structure exists at Site 1. A positive result would indicate the presence of a dome, and a negative result would indicate the absence of a dome. The test is not perfect, however. The test is highly accurate for detecting a dome; if there is a dome, the test shows a positive result 99% of the time. On the other hand, if there is no dome, the probability of a negative result is only 0.85. Thus, P(+ | Dome) = 0.99 and P(- | No Dome) = 0.85. Use these probabilities, the information given in the example, and Bayes' theorem to find the posterior probabilities P(Dome | +) and P(Dome | -). If the test gives a positive result, which site should be selected? Calculate expected values to support your conclusion. If the test result is negative, which site should be chosen? Again, calculate expected values.
Suppose you know that the amount a wine-drinker is willing to pay for a bottle of wine t years from now is $P(1+20(sqr(t))). Assuming continuous compounding and a prevailing interest rate of 5% per year, when is the best time to sell your wine?
An automorphism of a group G is an isomorphism from G to itself. A subgroup H of G is called characteristic, denoted Hchar G, if every automorphism of G maps H to itself (that is, φ(H) = H for all automorphisms φ of G). Prove that characteristic s..
A furniture manufacturing company planes to make three products - chairs, tables and desks from its available weekly resources, which consist of 400 cubic feet of timber and 500 man-hours of labor.
Assume that a monopolist sells a product with a total cost function TC = 1,200 + 0.5Q2 and a corresponding marginal cost function MC = Q.
A stem cell research project requires expensive specialized laboratory equipment. For this purpose, three pieces of equipment and their associated cash flows.
Your write-up should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. Change the price for chocolate to $2.10 and run the model once again. Explain how changing the price affects the..
Prove that T is a linear transformation on R 2 , and determine a 2 × 2 matrix form for T . What does T represent?
A telephone survey to determine viewer response to a new television show obtained the following data.
What is the optimal number of tables the company should produce during the current production cycle?
Two air tanks are connected by two parallel circular tubes, one having an inside diameter of 1 em and the other an inside diameter of 0.5 cm.
In 2008 the Better Business Bureau settled 75% of complaints it received (USA Today. March 2, 2009). Suppose you have been hired by the Better Business Bureau.
Explain in your own words what an uncertain quantity or random variable is. Why is the idea of an uncertain quantity important in decision analysis?
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