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

question 25

Essay

A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are shown below.
Payoff Table: $\begin{array}{ll}&\text { Alternative }\\\text { State of Nature }&\quad a_1\quad\quad a_2\quad\quad a_3\\\begin{array}{ll}s_1\\s_2\end{array}&\begin{array}{|lll|}\hline 20\quad&28\quad&33\quad \\32&29&25\\\hline\end{array}\end{array}$
Prior Probabilities:
P( $s _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.6.
Likelihood Probabilities: $\begin{array}{ll}&\quad I_1\quad\quad I_2\\\begin{array}{ll}s_1\\s_2\end{array}&\begin{array}{|ll|}\hline 0.95 & 0.05 \\0.08 & 0.92 \\\hline\end{array}\end{array}$
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:

Scarce Resources

Resources that are limited in availability and cannot fully meet the demands placed upon them by humans.

Collective Violence

Violence committed by larger groups of individuals and can encompass a wide range of acts, including social, political, and economic violence.

Charles Tilly

A renowned scholar in the fields of sociology and political science, known for his contributions to our understanding of social movements, democracy, and the history of Europe.

Directed Violence

Violence that is planned or intended to target specific individuals or groups.