[問題] 該不該作調查的問題(期望值)
問題:
Susan Su is not sure what she should do. She can either build a triplex,
build a duplex, or simply do nothing. Before doing so, she is considering the
possibility of conducting a study to gather additional information about the
rental market or not. If she gathers additional information, the results
could be either favorable or unfavorable rental market but it would cost her
$3,000 to gather the information. Susan believes that there is a 50-50 chance
that the information will be favorable. If the rental market is favorable,
Susan will earn $15,000 with the triplex or $5,000 with the duplex. Susan
doesn't have the financial resources to do both. With an unfavorable rental
market, however, Susan could lose $20,000 with the triplex or $10,000 with
the duplex. Without gathering additional information, Susan estimates that
the probability of a favorable rental market is 0.7. However, if a study is
conducted and the result turns out to be favorable, then the probability of a
favorable rental market would increase (from 0.7) to 0.9. Furthermore, given
an unfavorable result from the study, the probability of a favorable rental
market would decrease to 0.4. Of course, Susan could forget all of these
numbers and do nothing.
(a) Develop a decision tree for Susan Su.
(b) Label on the tree the decision alternatives, states of nature,
probabilities, and profits. Calculate all necessary values and put them on
your diagram.
What is your advice to Susan? [Note: You should put all necessary symbols in
your decision tree diagram to denote your decision process.
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我作到目前的部分 圖片有畫了
1.1.是說SUSAN認為調查結果有50%機會是出R，50%會是R*
2.2. SUSAN沒有做調查，估計將來實際是好市場F的機會是70%，壞市場F*的機會是30%
如果有做調查，調查結果是好的，而實際結果也是好的機會率，P(F|R) = 90%
結論想問的是說
該不該做調查
做調查的話，預期收益是$2750元，不做調查預期收益是$4500
但是2750是包括了3000元的調查費用
所以計算EVSI (expected value of sample information)的話，要把3000加回去
變成做調查比不做調查好1250元了
那麼應不應該做調查呢?
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