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:

Perspires

The act of sweating, a bodily function for cooling and detoxification.

Wernicke's Aphasia

A condition characterized by the inability to grasp the meaning of spoken words and sentences, while the production of language remains fluent but nonsensical.

Broca's Aphasia

A neurological condition characterized by difficulties in speech production and writing, often caused by damage to a specific area of the brain known as Broca's area.

Comprehend

To grasp mentally; understand.