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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