The Following Table Displays the Payoffs (In Thousands of Dollars)

question 36

Essay

The following table displays the payoffs (in thousands of dollars) for five different decision alternatives under three possible states of nature: $\begin{array} { ccc }&\text { Alternative }\\\text { State of Nature }& a_{1} & a_{2} & a_{3}& a_{4}& a_{5}\\s_{1} & \$ 100 & \$ 80 & \$ 35 & \$ 20 & \$ 0 \\s_{2} & \$ 70 & \$ 75 & \$ 55 & \$ 50 & \$ 15 \\s_{3} & -\$ 30 & \$ 0 & \$ 35 & \$ 55 & \$ 60\end{array}$
The prior probabilities of the states of nature are:
P( $S _ { 1 }$ ) = 0.2, P( $S _ { 2 }$ ) = 0.3, P( $S _ { 3 }$ ) = 0.5
a. Calculate the expected monetary value for each alternative with present information. What decision should be made using the EMV criterion?
b. Calculate the expected payoff with perfect information.
c. Calculate the expected value of perfect information.
d. Convert the payoff table to an opportunity loss table.
e. Calculate the expected opportunity loss for each act with present information. What decision should be made using the EOL criterion?

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Definitions:

Repolarization

The process by which cells, especially heart and nerve cells, restore their membrane potential to a resting state after depolarization.

Electrocardiogram

A diagnostic test that measures the electrical activity of the heart to assess its health and functionality.

Electrodes

Conductive materials that allow the flow of electrical current into or out of a medium, used in various electronic devices and medical applications.

Amplifier

An electronic device that increases the power, voltage, or current of a signal.