Exam 17: Decision Making

TABLE 17-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the average amount of time he needed to put in every week studying for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. 16 hours 8 hours 4 hours Easy Exam 40 60 80 Difficult Exam 100 50 0 -Referring to Table 17-6, what is the opportunity loss of spending 16 hours per week on average studying for the exam when the exam turns out to be easy?

TABLE 17-1 The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature. States A1 A2 A3 1 12 -2 8 2 4 10 5 $\text {where:}$$\quad$$\quad$ $\text {S1 is state of nature 1 }$$\quad$$\text {A1 is action alternative 1}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\text {S2 is state of nature 2}$$\quad$$\text { A2is action alternative 2}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {A3 is action alternative3 }$ -Referring to Table 17-1, if the probability of S1 is 0.5, what is the expected opportunity loss (EOL) for A3?

TABLE 17-5 $\text { The following payoff table showsprofits associated witha set of } 2 \text { alternatives under } 3 \text { possible events. }$ $\quad$ $\quad$ $\quad$ $\quad$ $\text {Action }$ Event A B 1 1000 1200 2 500 700 3 300 -200 Suppose that the probability of Event 1 is 0.2, Event 2 is 0.5, and Event 3 is 0.3. -Referring to Table 17-6, what is the expected opportunity loss of spending 8 hours per week on average studying for the exam?

TABLE 17-1 The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature. States A1 A2 A3 1 12 -2 8 2 4 10 5 $\text {where:}$$\quad$$\quad$ $\text {S1 is state of nature 1 }$$\quad$$\text {A1 is action alternative 1}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\text {S2 is state of nature 2}$$\quad$$\text { A2is action alternative 2}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {A3 is action alternative3 }$ -Referring to Table 17-1, if the probability of S1 is 0.5, what is the expected profit under certainty (EPUC )?

The risk seeker's curve represents the utility of one who enjoys taking risks. Therefore, the slope of the utility curve becomes______ for large dollar amounts.

The minimum expected opportunity loss is also equal to

Opportunity loss is the difference between the lowest profit for an event and the actual profit obtained for an action taken.

For a potential investment of $5,000, a portfolio has an EMV of $1,000 and a standard deviation of $100. What is the rate of return?

TABLE 17-1 The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature. States A1 A2 A3 1 12 -2 8 2 4 10 5 $\text {where:}$$\quad$$\quad$ $\text {S1 is state of nature 1 }$$\quad$$\text {A1 is action alternative 1}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\text {S2 is state of nature 2}$$\quad$$\text { A2is action alternative 2}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {A3 is action alternative3 }$ -Referring to Table 17-1, if the probability of S1 is 0.4, what is the probability of S2?

TABLE 17-6 A student wanted to find out the optimal strategy to study for a Business Statistics exam. He constructed the following payoff table based on the average amount of time he needed to put in every week studying for the course and the degree of difficulty of the exam. From the information that he gathered from students who had taken the course, he concluded that there was a 40% probability that the exam would be easy. 16 hours 8 hours 4 hours Easy Exam 40 60 80 Difficult Exam 100 50 0 -Referring to Table 17-6, the optimal strategy using the maximin criterion is to study 16 hours per week on average for the exam.

TABLE 17-2 The following payoff matrix is given in dollars. $\quad$ $\quad$ $\quad$ $\quad$ $\text {Action }$ Event A B 1 400 700 2 200 500 Suppose the probability of Event 1 is 0.5 and Event 2 is 0.5. -Referring to Table 17-2, what is the action with the preferable return to risk ratio?

TABLE 17-5 $\text { The following payoff table showsprofits associated witha set of } 2 \text { alternatives under } 3 \text { possible events. }$ $\quad$ $\quad$ $\quad$ $\quad$ $\text {Action }$ Event A B 1 1000 1200 2 500 700 3 300 -200 Suppose that the probability of Event 1 is 0.2, Event 2 is 0.5, and Event 3 is 0.3. -Referring to Table 17-5, what is the EVPI for this problem?

Blossom's Flowers purchases roses for sale for Valentine's Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine's Day can be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine's Day: 100, 200, or 400 dozen roses. What is the opportunity loss for buying 200 dozen roses and selling 100 dozen roses at the full price?

TABLE 17-2 The following payoff matrix is given in dollars. $\quad$ $\quad$ $\quad$ $\quad$ $\text {Action }$ Event A B 1 400 700 2 200 500 Suppose the probability of Event 1 is 0.5 and Event 2 is 0.5. -Referring to Table 17-2, what is the expected profit under certainty (EPUC )?

TABLE 17-4 A stock portfolio has the following returns under the market conditions listed below. Market Condition Probability Return Bull 0.4 \ 200 Stable 0.3 \ 100 Bear 0.3 -\ 100 -Referring to Table 17-4, what is the coefficient of variation?

TABLE 17-1 The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature. States A1 A2 A3 1 12 -2 8 2 4 10 5 $\text {where:}$$\quad$$\quad$ $\text {S1 is state of nature 1 }$$\quad$$\text {A1 is action alternative 1}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\text {S2 is state of nature 2}$$\quad$$\text { A2is action alternative 2}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {A3 is action alternative3 }$ -Referring to Table 17-1, if the probability of S1 is 0.5, what is the return to risk ratio for A1?

To calculate expected profit under certainty, we need to have perfect information about which event will occur.

TABLE 17-1 The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature. States A1 A2 A3 1 12 -2 8 2 4 10 5 $\text {where:}$$\quad$$\quad$ $\text {S1 is state of nature 1 }$$\quad$$\text {A1 is action alternative 1}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\text {S2 is state of nature 2}$$\quad$$\text { A2is action alternative 2}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {A3 is action alternative3 }$ -Referring to Table 17-1, if the probability of S1 is 0.2, what is the optimal alternative using EOL?

TABLE 17-1 The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature. States A1 A2 A3 1 12 -2 8 2 4 10 5 $\text {where:}$$\quad$$\quad$ $\text {S1 is state of nature 1 }$$\quad$$\text {A1 is action alternative 1}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\text {S2 is state of nature 2}$$\quad$$\text { A2is action alternative 2}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {A3 is action alternative3 }$ -Referring to Table 17-1, what is the best action using the maximin criterion?

Blossom's Flowers purchases roses for sale for Valentine's Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine's Day can be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine's Day: 100, 200, or 400 dozen roses. What is the payoff for buying and selling 400 dozen roses at the full price?