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You Are Given the Following Payoff Table \mid S1) = 0 \mid

question 46

Essay

You are given the following payoff table.  You are given the following payoff table.   Assume the following probability information is given. P(S<sub>1</sub>) = 0.45 P(I<sub>1</sub> \mid S<sub>1</sub>) = 0.7 P(I<sub>2</sub> \mid S<sub>1</sub>) = 0.3 P(S<sub>2</sub>) = 0.55 P(I<sub>1</sub> \mid S<sub>2</sub>) = 0.6 P(I<sub>2</sub> \mid S<sub>2</sub>) = 0.4  a.Find the values of P(I<sub>1</sub>) and P(I<sub>2</sub>). b.Determine the values of P(S<sub>1</sub> \mid I<sub>1</sub>), P(S<sub>2</sub> \mid I<sub>1</sub>), P(S<sub>1</sub> \mid I<sub>2</sub>), and P(S<sub>2</sub> \mid I<sub>2</sub>). c.Use the decision tree approach and determine the optimal strategy. What is the expected value of your solution? Assume the following probability information is given.
P(S1) = 0.45
P(I1 \mid S1) = 0.7
P(I2 \mid S1) = 0.3
P(S2) = 0.55
P(I1 \mid S2) = 0.6
P(I2 \mid S2) = 0.4
a.Find the values of P(I1) and P(I2).
b.Determine the values of P(S1 \mid I1), P(S2 \mid I1), P(S1 \mid I2), and P(S2 \mid I2).
c.Use the decision tree approach and determine the optimal strategy. What is the expected value of your solution?

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Definitions:

Income

The money received by an individual or organization, typically measured on a regular basis, for work or through investments.

MRS of Pencils

The marginal rate of substitution of pencils, indicating how much of another good a consumer is willing to give up for one more pencil.

Utility

In economics, a measure of satisfaction or happiness that a consumer derives from consuming goods and services.

Consumption Bundle

A collection of goods and services that an individual or household purchases over a given period.

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