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

question 3

Essay

A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are shown below.
Payoff Table: $\begin{array} { ccc }&\text { Alternative }\\\text { State of Nature }& a_{1} & a_{2} & a_{3}\\s_{1} & 80 & 120 & 90 \\s_{2} & 60 & 130 & 170 \\s_{3} & 200 & 140 & 100\end{array}$
Prior Probabilities:
P( $S _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.5, P( $S _ { 3 }$ ) = 0.1.
Likelihood Probabilities: $\begin{array}{ccc} & I_{1} & I_{2}& I_{3} \\s_{1} & 0.5 & 0.3 & 0.2 \\s_{2} & 0.2 & 0.6 & 0.2 \\s_{3} & 0.1 & 0.2 & 0.7\end{array}$ 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:

Personal Freedom

The power or right of an individual to act, speak, or think as one wants without hindrance or restraint, within the boundaries of the law or societal norms.

Self-Direction

Refers to the ability or quality of an individual to guide, control, and evaluate their own behavior and decisions.

Emotional Stability

A personality trait signifying the ability to remain calm and composed, and to handle stress or emotional challenges effectively.

Agreeableness

a personality trait that reflects a person's tendency to be compassionate, cooperative, and harmonious in their interactions with others.