For the Payoff Table Below,the Decision Maker Will Use P(s₁)=

question 38

Essay

For the payoff table below,the decision maker will use P(s₁)= .15,P(s₂)= .5,and P(s₃)= .35. $$\begin{array} { c | r c c } && { \text { State of Nature } } \\\text { Decision } & { s _ { 1 } } & s _ { 2 } & s _ { 3 } \\\hline d _ { 1 } & - 5000 & 1000 & 10,000 \\d _ { 2 } & - 15,000 & - 2000 & 40,000\end{array}$$
a.What alternative would be chosen according to expected value?
b.For a lottery having a payoff of 40,000 with probability p and 15,000 with probability (1  p), the decision maker expressed the following indifference probabilities. $$\begin{array} { r c } \text { Payoff } & \text { Probability } \\\hline 10,000 & .85 \\1000 & .60 \\- 2000 & .53 \\- 5000 & .50\end{array}$$ Let U(40,000) = 10 and U(15,000) = 0 and find the utility value for each payoff.
c.What alternative would be chosen according to expected utility?

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Definitions:

Normal Distribution

In this type of distribution, occurrences of data are more frequent near the mean and decrease in frequency as they move away from the mean, with the distribution being symmetric.

Sampling Distribution

The probability distribution of a statistic based on random samples from a population, used to estimate population parameters.

Standard Deviation

An indicator of the degree to which a dataset's values vary or are dispersed, showing the extent of deviation from the average.

Normal Distribution

A distribution of probabilities that is even on both sides of the mean, illustrating that values near the mean happen more often than values at a greater distance from the mean.