Problem 1. Men and women arrive as couples at a fitness club. Men’s weights are known to be normally distributed with a mean of 180 and a standard deviation of 25 pounds. Women’s weights are also normally distributed with a mean of 135 and a standard deviation of 15 pounds. Use Monte Carlo simulation to determine:
(1) The average combined weight of the two partners.
(2) The average weight of the lighter of the partners.
(3) The average difference between the weights of the two partners.
(4) The percentage of time that the woman is the heavier individual.
Be certain to use sufficient replications (i.e., sample size) so that you are fairly sure of your answers.
Assuming the parameters given are correct, suggest several reasons why the answers suggested by your simulation might not be the same as data from actual on-site observations?
Problem 2. The following payoff table provides profits based on various possible decision alternatives and various levels of demand.
1. Men and women arrive as couples at a fitness club. Men’s weights are known to be normally distributed with a mean of 180 and a standard deviation of 25 pounds. Women’s weights are also normally distributed with a mean of 135 and a standard deviation of 15 pounds. Use Monte Carlo simulation to determine:
(1) The average combined weight of the two partners.
(2) The average weight of the lighter of the partners.
(3) The average difference between the weights of the two partners.
(4)The percentage of time that the woman is the heavier individual.
Be certain to use sufficient replications (i.e., sample size) so that you are fairly sure of your answers.
Assuming the parameters given are correct, suggest several reasons why the answers suggested by your simulation might not be the same as data from actual on-site observations?
2. The following payoff table provides profits based on various possible decision alternatives and various levels of demand.
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States of Nature
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Demand
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Alternatives
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Low
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Medium
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High
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Alternative 1
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80
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120
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140
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Alternative 2
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90
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90
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90
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Alternative 3
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50
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70
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150
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The probability of a low demand is 0.4, while the probability of a medium and high demand is each 0.3.
(a) What decision would an optimist make? Why?
(b) What decision would a pessimist make? Why?
(c) What decision would you make? Why?
(c) What is the highest possible expected monetary value?
(d) Calculate the expected value of perfect information for this situation.