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

Question 48

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 a1a2a3s1202833s2322925\begin{array} { ccc }&\text { Alternative }\\\text { State of Nature }& a_{1} & a_{2} & a_{3}\\s_{1} & 20 & 28 & 33 \\s_{2} & 32 & 29 & 25\end{array}
Prior Probabilities:
P( S1S _ { 1 } ) = 0.4, P( S2S _ { 2 } ) = 0.6.
Likelihood Probabilities: I1I2s10.950.05s20.080.92\begin{array}{ccc} & I_{1} & I_{2} \\s_{1} & 0.95 & 0.05 \\s_{2} & 0.08 & 0.92\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) = ...

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