The Following Table Displays the Payoffs (In Thousands of Dollars)

question 20

Essay

The following table displays the payoffs (in thousands of dollars) for five different decision alternatives under three possible states of nature: $\begin{array}{ll}&\text { Alternative(Decision) }\\\text { State of Nature }&\quad a_1\quad\quad a_2\quad\quad a_3\quad\quad a_4\quad\quad a_5\\\begin{array}{ll}s_1\\s_2\\s_3\end{array}&\begin{array}{|lll|}\hline\$100\quad\$80\quad\quad \$35\quad\$20\quad\$0\\\$70\quad\quad\$75\quad\$55\quad\$50\quad\$15\\-\$30\quad\quad\$0\quad\$35\quad\$55\quad\$60\\\hline\end{array}\end{array}$
The prior probabilities of the states of nature are:
P( $s _ { 1 }$ ) = 0.2, P( $S _ { 2 }$ ) = 0.3, P( $S _ { 3 }$ ) = 0.5
a. Calculate the expected monetary value for each alternative with present information. What decision should be made using the EMV criterion?
b. Calculate the expected payoff with perfect information.
c. Calculate the expected value of perfect information.
d. Convert the payoff table to an opportunity loss table.
e. Calculate the expected opportunity loss for each act with present information. What decision should be made using the EOL criterion?

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