A Payoff Table Is Shown Below The Following Prior Probabilities Are Assigned to the States of }\\\text

question 39

Essay

A payoff table is shown below: $\begin{array}{ll}&\text { Alternative }\\\text { State of Nature }&\quad a_1\quad\quad a_2\quad\quad a_3\quad\quad a_4\\\begin{array}{ll}s_1\\s_2\end{array}&\begin{array}{|llll|}\hline 7\quad\quad&0\quad\quad&4\quad&6 \\2&4&3&5\\\hline\end{array}\end{array}$
The following prior probabilities are assigned to the states of nature:
P( $s _ { 1 }$ ) = 0.3, P( $S _ { 2 }$ ) = 0.7.
a. Calculate the expected monetary value for each act with present information. What decision should be made using the EMV criterion?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each act with present information. What decision should be made using the EOL criterion?
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?

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Definitions:

Water Solubility

The ability of a substance to dissolve in water, forming a homogeneous solution at a given temperature and pressure.

Chitin

Nitrogen-containing polysaccharide that composes fungal cell walls and arthropod exoskeletons.

Strengthens

Refers to making something stronger or more effective.

Structure

The arrangement or organization of parts to form a complex entity, observable in architecture, molecules, and living organisms.