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

question 1

Essay

A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are shown below.
Payoff Table: $\begin{array}{ll}&\text { Alternative }\\\text { State of Nature }&\quad a_1\quad\quad a_2\quad\quad a_3\\\begin{array}{ll}s_1\\s_2\\s_3\end{array}&\begin{array}{|lll|}\hline80\quad&120\quad&90\quad \\60&130&170\\200&140&100\\\hline\end{array}\end{array}$
Prior Probabilities:
P( $s _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.5, P( $S _ { 3 }$ ) = 0.1.
Likelihood Probabilities: $\begin{array}{ll}&\quad I_1\quad\quad I_2\quad\quad I_3\\\begin{array}{ll}s_1\\s_2\\s_3\end{array}&\begin{array}{|lll|}\hline0.5\quad&0.3\quad&0.2\quad \\0.2&0.6&0.2\\0.1&0.2&0.7\\\hline\end{array}\end{array}$
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?

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Definitions:

Sterile Field

A specific area free of microorganisms to maintain sterility during medical procedures or experiments.

Incision and Drainage (I&D)

A medical procedure involving the cutting of the skin and the removal of fluid from a wound or an abscess.

Localized Infection

An infection that is restricted to a specific part of the body and does not spread.

Abscess

A localized collection of pus within tissues, organs, or spaces in the body, typically caused by an infection.