SCENARIO 20-1
The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature.

-Referring to Scenario 20-1,if the probability of S1 is 0.5,then the coefficient of variation for A1 is
A)23.1%
B)50%
C)150%
D)200%

Question

SCENARIO 20-1
The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature.

-Referring to Scenario 20-1,if the probability of S1 is 0.5,then the coefficient of variation for A1 is
A)23.1% 
B)50% 
C)150% 
D)200%

Quizplus · Accepted Answer

To find the coefficient of variation for A1, we need to first calculate the expected value and standard deviation for A1.

Expected value for A1 = (0.5*160) + (0.5*60) = 110

Variance for A1 = (0.5*(160-110)^2) + (0.5*(60-110)^2) = 2500 
Standard deviation for A1 = sqrt(variance) = 50

Coefficient of variation for A1 = (standard deviation / expected value) * 100% = (50 / 110) * 100% = 45.45%, which is closest to choice B (50%).

To find the best choice(s), we can use the maximax criterion, which selects the alternative with the highest possible payoff under the best state of nature.

Under S1, A1 has the highest payoff of 160. Under S2, A3 has the highest payoff of 180.

Therefore, the best choice is A1 under S1 and A3 under S2.

SCENARIO 20-1 The Following Payoff Table Shows Profits Associated with a Set