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

question 7

Essay

A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are shown below.
Payoff Table: $\begin{array}{ll}&\text { Alternative }\\\text { State of Nature }&\quad a_1\quad\quad a_2\quad\quad a_3\\\begin{array}{ll}s_1\\s_2\end{array}&\begin{array}{|lll|}\hline 0.95 & 0.05&33 \\0.08 & 0.92 &25\\\hline\end{array}\end{array}$
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) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 1 }$ .
B) Use the posterior probabilities from a. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*.
C) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 2 }$ .
D) Use the posterior probabilities from c. to recalculate the expected monetary value of each act, then determine the optimal act and the $\text { EMV } ^ { * }$ .
E) Use your answers to parts a. to d. to calculate the expected monetary value with additional information.
F) Calculate the expected value of sample information.

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Definitions:

Control

The power to influence or direct people's behavior or the course of events.

Implicit Assumption

An unstated belief or premise that influences attitudes, actions, and decisions without explicit acknowledgment.

Behavioral Approach

A methodology focusing on understanding and modifying individuals' behaviors through studying their actions and reactions.

Interpersonal Trust

A psychological state comprising the intention to accept vulnerability based upon positive expectations of the intentions or behavior of another.