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

Essay

A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are shown below.
Payoff Table: $\begin{array} { ccc }&\text { Alternative }\\\text { State of Nature }& a_{1} & a_{2} & a_{3}\\s_{1} & 80 & 120 & 90 \\s_{2} & 60 & 130 & 170 \\s_{3} & 200 & 140 & 100\end{array}$
Prior Probabilities:
P( $S _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.5, P( $S _ { 3 }$ ) = 0.1.
Likelihood Probabilities: $\begin{array}{ccc} & I_{1} & I_{2}& I_{3} \\s_{1} & 0.5 & 0.3 & 0.2 \\s_{2} & 0.2 & 0.6 & 0.2 \\s_{3} & 0.1 & 0.2 & 0.7\end{array}$ 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?