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

question 10

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.

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Definitions:

Pounds Sterling

The official currency of the United Kingdom, which is also used in other territories and dependencies.

Temporal Method

An exchange rate conversion method used in financial reporting where monetary assets and liabilities are converted at current rates and non-monetary items at historical rates.

Canadian Dollars

Canadian dollars (CAD) refer to the official currency of Canada, which is used for all transactions within the country.

Translation Gain/Loss

The gain or loss resulting from the conversion of foreign currency amounts into the functional currency of a business during the consolidation of financial statements.