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A Payoff Table, the Prior Probabilities for Two States of Nature

Question 46

Essay

A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are shown below.
Payoff Table:  Alternative  State of Nature a1a2a3s1s2202833322925\begin{array}{ll}&\text { Alternative }\\\text { State of Nature }&\quad a_1\quad\quad a_2\quad\quad a_3\\\begin{array}{ll}s_1\\s_2\end{array}&\begin{array}{|lll|}\hline 20\quad&28\quad&33\quad \\32&29&25\\\hline\end{array}\end{array}
Prior Probabilities:
P( s1s _ { 1 } ) = 0.4, P( S2S _ { 2 } ) = 0.6.
Likelihood Probabilities: I1I2s1s20.950.050.080.92\begin{array}{ll}&\quad I_1\quad\quad I_2\\\begin{array}{ll}s_1\\s_2\end{array}&\begin{array}{|ll|}\hline 0.95 & 0.05 \\0.08 & 0.92 \\\hline\end{array}\end{array}
a. Determine the EMV decision.
b. Set up the opportunity loss table.
c. Determine the EOL decision.
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?

Correct Answer:

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a. EMV ( blured image ) = (0.4)(20) + (0.6)(32) = 27...

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