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

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. 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 $\mathrm { EMV } ^ { * }$ .
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.