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

question 20

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. 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 EMV*.
e. Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 3 }$ .
f. Use the posterior probabilities from e. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*.
g. Use your answers to parts a. to f. to calculate the expected monetary value with additional information.
h. Calculate the expected value of sample information.

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Definitions:

Betty Friedan

An influential American feminist, writer, and activist best known for her 1963 book "The Feminine Mystique," which challenged the traditional roles of women in society.

Majority-minority

A demographic term used when the combined minority populations surpass the number of the majority population.

Pluralistic

A condition or system in which two or more states, groups, principles, sources of authority, etc., coexist.

Minority Group

A social group that is systematically denied the same access to power and resources available to society’s dominant groups though its members are not necessarily fewer in number than the dominant groups.