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

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. 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.