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

question 41

Essay

A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are shown below.
Payoff Table: $\begin{array}{ll}&\text { Alternative }\\\text { State of Nature }&\quad a_1\quad\quad a_2\quad\quad a_3\\\begin{array}{ll}s_1\\s_2\\s_3\end{array}&\begin{array}{|lll|}\hline80\quad&120\quad&9\quad \\60&130&170\\200&140&100\\\hline\end{array}\end{array}$
Prior Probabilities:
P( $s _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.5, P( $S _ { 3 }$ ) = 0.1.
Likelihood Probabilities: $\begin{array}{ll}&\quad I_1\quad\quad I_2\quad\quad I_3\\\begin{array}{ll}s_1\\s_2\\s_3\end{array}&\begin{array}{|lll|}\hline0.5\quad&0.3\quad&0.2\quad \\0.2&0.6&0.2\\0.1&0.2&0.7\\\hline\end{array}\end{array}$
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 EMV*.
E) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 3 }$ .
F) Use the posterior probabilities from e. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*.
G) Use your answers to parts a. to f. to calculate the expected monetary value with additional information.
H) Calculate the expected value of sample information.

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Definitions:

Designated Groups

Categories of people identified for special consideration or protection under laws or policies, often related to employment equity.

Valuable

Describes something that holds great worth or importance, often due to its utility, rarity, or contribution towards achieving a goal.

Organized

Having a structured and systematic arrangement; often refers to entities or groups that are systematically coordinated, such as labor unions.

Efficient

The ability to achieve maximum productivity with minimum wasted effort or expense, often related to processes, systems, or machines.