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

question 8

Essay

A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are shown below.
Payoff Table: $\begin{array} { ccc }&\text { Alternative }\\\text { State of Nature }& a_{1} & a_{2} & a_{3}\\s_{1} & 20 & 28 & 33 \\s_{2} & 32 & 29 & 25\end{array}$
Prior Probabilities:
P( $S _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.6.
Likelihood Probabilities: $\begin{array}{ccc} & I_{1} & I_{2} \\s_{1} & 0.95 & 0.05 \\s_{2} & 0.08 & 0.92\end{array}$ 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:

Critical Period

A specific time in development when the organism is particularly sensitive to environmental stimuli, and thus has an enhanced capacity for learning or development in a particular area.

Visual Stimulation

The process of using visual cues or images to engage the visual sense, often for entertainment, education, or therapeutic purposes.

Behavior Genetics

The field of study focused on understanding how genetic and environmental factors influence individual differences in behavior.

Scientific Usage

The application of scientific knowledge, methods, and terminologies in specific fields or research activities.