Homework Help is Here – Start Your Trial Now!
Math
Probability
a) Calculate the posterior probabilities P (State = Oil | Finding = USS) and P (State = Dry | Finding = USS), ifthe founding of the seismic survey is unfavorable seismic soundings (USS), by using Bayes" theorem. b) Calculate the posterior probabilities P (State = Oil | Finding = FSS) and P (State = Dry | Finding = FSS), if the seismie survey gives favorable seismic soundings (FSS), by using Bayes' theorem. c) Draw the probability tree diagram for the full problem by showing all the probabilities leading to the calculation of each posterior probability of the state of nature given the finding of the seismic survey. d) Calculate the expected payoffs and determine the optimal action if finding is USS. c) Calculate the expected payoffs and determine the optimal action if finding is FSS. f) Calculate the expected value of perfect information (EVPI). According to the result, determine if to proceed with the seismic survey is worthwhile. g) Calculate the expected value of experimentation (EVE). According to the result, determine if to proceed with the seismic survey is worthwhile.

a) Calculate the posterior probabilities P (State = Oil | Finding = USS) and P (State = Dry | Finding = USS), ifthe founding of the seismic survey is unfavorable seismic soundings (USS), by using Bayes" theorem. b) Calculate the posterior probabilities P (State = Oil | Finding = FSS) and P (State = Dry | Finding = FSS), if the seismie survey gives favorable seismic soundings (FSS), by using Bayes' theorem. c) Draw the probability tree diagram for the full problem by showing all the probabilities leading to the calculation of each posterior probability of the state of nature given the finding of the seismic survey. d) Calculate the expected payoffs and determine the optimal action if finding is USS. c) Calculate the expected payoffs and determine the optimal action if finding is FSS. f) Calculate the expected value of perfect information (EVPI). According to the result, determine if to proceed with the seismic survey is worthwhile. g) Calculate the expected value of experimentation (EVE). According to the result, determine if to proceed with the seismic survey is worthwhile.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
icon
Concept explainers
Question

course name : stochastic models

please i nead to solve all the steps

 

thanks & best regards

Question: The GOFERBROKE COMPANY owns a tract of land that may contain oil. A consulting geologist has reported to management that she believes there is 3 chances in 10 of oil. Because of this prospect, another oil company has offered to purchase the land for $127,300. However, Goferbroke is considering holding the land in order to drill for oil itself. The cost of drilling is $152,760. If oil is found, the resulting expected revenue will be $865,640, so the company's expected profit (after deducting the cost of drilling) will be $712,880. A loss of $152,760 (the drilling cost) will be incurred if the land is dry (no oil). Table 1 summarizes these data. TABLE 1 Prospective profits for the Goferbroke Company Status of Land Payoff Alternative Dry $712,880 $127,300 - $152,760 $127,300 D for of Sell the land Chance of status 3 in 10 7 in 10 However, before deciding whether to drill or sell, the company wants to be conducted a detailed seismic survey of the land to obtain a better estimate of the probability of finding oil. The survey cost is $40,000. A seismic survey obtains seismic soundings that indicate whether the geological structure is favorable to the presence of oil. We will divide the possible findings of the survey into the following two categories:
Transcribed Image Text:Question: The GOFERBROKE COMPANY owns a tract of land that may contain oil. A consulting geologist has reported to management that she believes there is 3 chances in 10 of oil. Because of this prospect, another oil company has offered to purchase the land for $127,300. However, Goferbroke is considering holding the land in order to drill for oil itself. The cost of drilling is $152,760. If oil is found, the resulting expected revenue will be $865,640, so the company's expected profit (after deducting the cost of drilling) will be $712,880. A loss of $152,760 (the drilling cost) will be incurred if the land is dry (no oil). Table 1 summarizes these data. TABLE 1 Prospective profits for the Goferbroke Company Status of Land Payoff Alternative Dry $712,880 $127,300 - $152,760 $127,300 D for of Sell the land Chance of status 3 in 10 7 in 10 However, before deciding whether to drill or sell, the company wants to be conducted a detailed seismic survey of the land to obtain a better estimate of the probability of finding oil. The survey cost is $40,000. A seismic survey obtains seismic soundings that indicate whether the geological structure is favorable to the presence of oil. We will divide the possible findings of the survey into the following two categories:
USS: Unfavorable seismic soundings; oil is fairly unlikely. FSS: Favorable scismic soundings; oil is fairly likcly. Based on past experience, if there is oil, then the probability of unfavorable seismic soundings is P(USS | State = Oil) = 0.35, P(USS | State = Oil) = 0.65, Similarly, if there is no oil (i.c., the true state of nature is Dry), then the probability of unfavorable scismic soundings is estimated to be P(USS | State = Dry) = 0.8, P(USS | State = Dry) =0.2. By using the given data; a) Calculate the posterior probabilities P (State = Oil | Finding = USS) and P (State = Dry | Finding = USS), if the founding of the scismic survey is unfavorable seismic soundings (USS), by using Bayes theorem. b) Calculate the posterior probabilities P (State = Oil | Finding = FSS) and P (State = Dry | Finding = FSS), if the scismie survey gives favorable seismie soundings (FSS), by using Bayes' theorem. c) Draw the probability tree diagram for the full problem by showing all the probabilities leading to the calculation of cach posterior probability of the state of nature given the finding of the scismic survey. d) Calculate the expected payoffs and determine the optimal action if finding is USS. e) Calculate the expected payoffs and determine the optimal action if finding is FSS. f) Calculate the expected value of perfect information (EVPI). According to the result, determine if to proceed with the seismic survey is worthwhile. g) Calculate the expected value of experimentation (EVE). According to the result, determine if to proceed with the seismic survey is worthwhile.
Transcribed Image Text:USS: Unfavorable seismic soundings; oil is fairly unlikely. FSS: Favorable scismic soundings; oil is fairly likcly. Based on past experience, if there is oil, then the probability of unfavorable seismic soundings is P(USS | State = Oil) = 0.35, P(USS | State = Oil) = 0.65, Similarly, if there is no oil (i.c., the true state of nature is Dry), then the probability of unfavorable scismic soundings is estimated to be P(USS | State = Dry) = 0.8, P(USS | State = Dry) =0.2. By using the given data; a) Calculate the posterior probabilities P (State = Oil | Finding = USS) and P (State = Dry | Finding = USS), if the founding of the scismic survey is unfavorable seismic soundings (USS), by using Bayes theorem. b) Calculate the posterior probabilities P (State = Oil | Finding = FSS) and P (State = Dry | Finding = FSS), if the scismie survey gives favorable seismie soundings (FSS), by using Bayes' theorem. c) Draw the probability tree diagram for the full problem by showing all the probabilities leading to the calculation of cach posterior probability of the state of nature given the finding of the scismic survey. d) Calculate the expected payoffs and determine the optimal action if finding is USS. e) Calculate the expected payoffs and determine the optimal action if finding is FSS. f) Calculate the expected value of perfect information (EVPI). According to the result, determine if to proceed with the seismic survey is worthwhile. g) Calculate the expected value of experimentation (EVE). According to the result, determine if to proceed with the seismic survey is worthwhile.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Correlation, Regression, and Association
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS