1. Calculate the joint probabilities of P(P, g) P(P, p) P(N, g) P(N, p) 2. Using the estimated joint probabilities, comp
Posted: Wed May 11, 2022 8:16 pm
1. Calculate the joint probabilities of
P(P, g)
P(P, p)
P(N, g)
P(N, p)
2. Using the estimated joint probabilities, compute the posterior
probabilities using Bayes’ formula.
P(g|P)
P(p|P)
P(g|N)
P(p|N)
3. By obtaining the additional information of a positive report
from the analyst, the investor can revise the prior probability of
good conditions (i.e., 0.6).
What is the revised probability that good economic conditions
will occur?
A real estate investor is considering three alternative investments, which will occur under one of the two possible economic conditions (states of nature) as shown in the table. Decision Good economic conditio Poor economic conditior EV Apartment building $50,000 $30,000 42000 Office building 100,000 (40,000) 44000 Warehouse 30,000 10,000 22000 0.6 0.4 72,000 EVwPI EVwoPI EVPI 44,000 28.000 Given the probability distribution of the two-state of nature. EV is $44.000. The computed expected value of perfect information suggests that the investor would be willing to pay up to $28.000 for information about the state of nature, depending on how close to perfect the information was. Now suppose that the investor has decided to hire a professional economic analyst who will provide additional information about future economic conditions. The analyst is constantly researching the economy, and the results of this research are what the investor will be purchasing. The economic analyst will provide the investor with a report predicting one of two outcomes. The report will be either positive or negative. Positive = good economic conditions are most likely to prevail in the future
Negative = poor economic conditions will probably occur. Based on the analyst's past record in forecasting future economic conditions, the investor has determined conditional probabilities of the different report outcomes, given the occurrence of each state of nature in the future. P P N 6.AZ good economic conditions poor economic conditions positive economic report negative economic report The prior probabilities of each state of nature (good or poor economic conditions) will occur in the future are P(g) = 0.6 P(p) -0.4 The conditional probability of each reported outcome, given the occurrence of each state of nature. P(Pg) - 0.85 P(N2) = 0.15 P(Pp) = 0.08 P(Np) = 0.92 1. Calculate the joint probabilities of P(Pg) P(PP) P(8) PNP) 2. Using the estimated joint probabilities, compute the posterior probabilities using Bayes' formula P(g/P) P(PP) P(g/N)
P(p/N) 3. By obtaining the additional information of a positive report from the analyst, the investor can revise the prior probability of good conditions (L.e., 0.6). What is the revised probability that good economic conditions will occur?
P(P, g)
P(P, p)
P(N, g)
P(N, p)
2. Using the estimated joint probabilities, compute the posterior
probabilities using Bayes’ formula.
P(g|P)
P(p|P)
P(g|N)
P(p|N)
3. By obtaining the additional information of a positive report
from the analyst, the investor can revise the prior probability of
good conditions (i.e., 0.6).
What is the revised probability that good economic conditions
will occur?
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Negative = poor economic conditions will probably occur. Based on the analyst's past record in forecasting future economic conditions, the investor has determined conditional probabilities of the different report outcomes, given the occurrence of each state of nature in the future. P P N 6.AZ good economic conditions poor economic conditions positive economic report negative economic report The prior probabilities of each state of nature (good or poor economic conditions) will occur in the future are P(g) = 0.6 P(p) -0.4 The conditional probability of each reported outcome, given the occurrence of each state of nature. P(Pg) - 0.85 P(N2) = 0.15 P(Pp) = 0.08 P(Np) = 0.92 1. Calculate the joint probabilities of P(Pg) P(PP) P(8) PNP) 2. Using the estimated joint probabilities, compute the posterior probabilities using Bayes' formula P(g/P) P(PP) P(g/N)
P(p/N) 3. By obtaining the additional information of a positive report from the analyst, the investor can revise the prior probability of good conditions (L.e., 0.6). What is the revised probability that good economic conditions will occur?