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

question 3

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. Determine the EMV decision.
b. Set up the opportunity loss table.
c. Determine the EOL decision.
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?

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Definitions:

Merchandise Inventory

Goods a company holds for the purpose of resale in the normal course of business.

Product Costs

These are costs that are directly associated with the creation of a product, including direct materials, direct labor, and manufacturing overhead.

Period Costs

Expenses incurred by a business that are not directly tied to the production process and are charged to the period in which they occur.

Variable Cost

Expenditures that are directly correlated with the volume of production or output level.